There isn't really a straight forward, simple answer to this as it could depend on who the enslaver was, but either way the marriage would have no legal validity, and always risked a forced rupture by sale. I've written previously on this topic here looking the breaking apart of enslaved families in the antebellum South, with estimates suggesting that roughly ⅓ of enslaved marriages would be forced to end in that way. But that isn't quite your question, so I'll expand a little on the nature of marriage itself within the system of enslavement present in the American South.

Most commonly, there would be something in-between your two propositions, with an enslaved person not able to marry freely, but not forced into one either. Permission often would need to be sought though, especially in the case of a cross-plantation marriage, which we'll return to, but it also ought to be emphasized that enslaved marriages were, in a sense, dehumanized by the enslaver. I don't mean this merely in the sense that they were not granted legal recognition, but in that enslavers would often assert that the enslaved were incapable of the same level of true affection and familial attachment that whites were. This of course was not true, but it was a convenient lie enslavers told themselves as they broke up such families, and one rife with contradictions in the behavior of enslavers as well. To be sure, some Christian reformers in the last decades of American slavery did try to argue for reforms of the slave codes, including legal recognition of marriage to as to make slavery more 'Biblical', but such attempts never came to fruition, clashing with the interests of the planter class and their property rights.

Anyways though, generally speaking, marriages were not strongly policed by the enslavers, and evidence suggests that parents of younger enslaved persons often could be the principal drivers of matchmaking, with enslaved marriages usually occurring in the mid-to-late teens, and the enslavers themselves then granting their permission after a match had been arranged, sometimes even being the one to conduct the service. This isn't to say that marriages weren't forced, but despite the tyranny of a slave society, this was one facet of life where it was not the common approach, although to be sure estimates of ~10% of marriages being arranged and forced by the enslaver is hardly a pittance either.

While a large plantation could support several families and allow for intermarriage, cross-plantation unions were common with smaller plantations, or farmer who owned only one or two enslaved persons, as it meant that to marry they likely would need to find a spouse elsewhere. Such cross-plantation marriages required permission from the enslavers of both parties, which could create complications if friction existed. There was no guarantee it would be granted, and while many enslavers - especially with larger plantations - prohibited such marriages and would not allow them, it was hard to avoid allowing entirely. Although it would vary by region, roughly 1/4 to ⅓ of enslaved marriages were between enslaved persons with two different masters, but it could be much higher in some regions where large plantations were uncommon, such as Missouri where more than half of all enslaved marriages were so.

This kind of marriage meant that at least one of the enslaved persons - usually the husband - would be making frequent visits away from his own plantation to that of his wife. This would be allowable with a pass, but all the same many enslavers were not quite happy with such things however necessary they might be, as in their mind it granted a degree of independence to their human property that could be dangerous. Other enslavers though took an opposite tack, believing that granting a little independence, such as with a cross-plantation marriage

It also wasn't merely their own developing independence, but the fears of cross-plantation communication - and the specter of servile insurrection that came with organization - that such visits facilitated generally. The 'grapevine telegraph', as it was known, existed regardless and enslaved persons would often travel illicitly, without a pass and at risk of capture and punishment by slave patrols, to pass news between plantations, but enslaved men visiting their wives provided particular danger there, as they could carry information under a pass, and with regularity.

It should be noted though that husbands would often visit their wives even without a pass. It was rare to have complete, free-reign to visit at will, passes being limited to perhaps one night a week, and likewise authorized visits few. For the enslavers it was, in the end, a simple matter of control, and balancing those fears of developing independence. But for an enslaved husband, it was of course a cruel imposition. As such sneaking away when unauthorized for clandestine visits was common, and more importantly, it was a way for the man - in the face of white attempts to emasculate him, whether implicitly by stripping him of patriarchal power in his relationship, or explicitly by the sexual violation enslaved women - to prove and assert his masculinity, not only to his wife, but also to the other men around him. An enslaver being too restrictive in their allowance for visits also could, in the end, be an impetus for the choice to run away.

As for the marriage itself, the way it was administered varied in solemnity. While one the one hand claiming enslaved marriages lacked deep meaning and affection, white enslavers at the same time recognized the importance of such bonds in maintaining social order within their enslaved communities and how marriage could help provide stability... not to mention more enslaved children down the line. As such, wedding ceremonies, despite not actually being recognized by law, often were still granted social recognition with an administering of vows by a white justice of the peace, or a white minister, or even their enslaver himself.

This of course could vary greatly based on the particulars of the enslaver, and plenty more ceremonies were conducted by black officiants as well, but it helps to illustrate those 'rife contradictions' mentioned prior. And of course, the enslaver's presence in the ceremony came not without an implicit reminder that this was happening because they had allowed it. For the enslaved themselves, while they generally welcomed the involvement of whites in the ceremony, for them it was the hopeful reminder that whatever the rhetoric, such unions were real and meaningful, and a reminder to the enslavers not to break them apart. As Kaye aptly sums it up:

A wedding, though not a ritual, seemed from the slaves’ standpoint to symbolically mediate the conflict between slave owners’ property rights and bonds between spouses. Marriage held out a promise of permanence, however implicit, and slaves did everything in their power to hold owners to that promise.

This didn't stop all would-be couples though, even if it might have for some. For the enslaved persons themselves, they didn't actually consider the enslaver's blessing a necessary component of their union, even if it was an important one, and some at least went through the rituals without permission. Kaye recounts one such example where an enslaver granted permission to an enslaved woman he owned on the condition that the prospective groom, on another plantation, get permission as well. The man was unable to get it, so the enslaver withdrew his permission. They married anyways, and although the enslaver considered selling her South as punishment, her entreaties were successful in convincing him to sell her to the enslaver of her husband instead.

That is perhaps a good place to wrap up as I think it helps really flesh out the perspective of the enslaved themselves. Marriage might not have been recognized by law, it might have been controlled by the enslavers, and looked down upon by white society in general, but for the enslaved people themselves, none of that really mattered, and marriage, as in many other aspects of their lives, offered windows for small acts of resistance, and assertion of their own humanity.

Sources

Franklin, John Hope & Loren Schweninger. Runaway Slaves: Rebels on the Plantation. Oxford University Press, 2000.

Genovese, Eugene D. Roll, Jordan, Roll: The World the Slaves Made. Vintage Books, 1976.

Kaye, Anthony E. Joining Places: Slave Neighborhoods in the Old South. The University of North Carolina Press, Jan 2007.

Lussana, Sergio A.. My Brother Slaves: Friendship, Masculinity, and Resistance in the Antebellum South. University Press of Kentucky, 2016.

Slaves had no real rights or agency when it came to marriage or much of anything else. Slaves couldn’t legally marry because they were legally defined as property and had no capacity to enter into legally enforceable contracts. So there weren’t too many “arranged marriages” organized by their masters. There are lots of accounts of slaves asking for and receiving permission to “get married” but that mostly meant they could live together, and it wasn’t legally binding and didn’t protect them from anything. Their kids were still born property and their owner could split them up at any time.

And the brutal reality of slavery in the US is that it was an industry that thrived and relied on systematic mass forced breeding, particularly after the abolition of the transatlantic slave trade in 1807. Just like with horses, there were “arranged marriages” between studs and mares, but that was solely for the purpose of procreation, they might never see each other again, and their child was a product to be sold. Plantations would even rent out their studs, or “stockmen” to other plantations to go and impregnate all their female slaves. Some women would be turned into “breeders” as soon as they hit puberty and would be used to pump out babies until they died or aged out. According to Peter Kolchin, there was an average birthrate of 7 children per slave woman. Even slaves that had relationships sanctioned by their masters might be forced to reproduce with others on a whim. If you were a female slave you were almost guaranteed to be raped and impregnated throughout your life and then your children would likely be taken from you and sold either once they stop nursing or once they become useful. Best case scenario would be that the plantation owner is breeding and hoarding slaves as a capital asset, in which case you’d get to raise your kids or at least know they were still on the plantation.

I think many people in America want to think that slavery in the US wasn’t that bad and try to look back on it and seek out positives to point to, but unfortunately “marriage” is maybe one of the darkest aspects of the entire plunderbund. For every individual anecdote of a nice master letting his slaves “marry” and live in their own house and raise their kids on the property, there are thousands of ignored cases of systematic inescapable and unending rape and abuse happening to these people for their entire lives for hundreds of years.

EDIT: Was just having a gander at wiki to see how off I was and I found a good quote related to how slave women would resist attempts at the kind of “arranged marriage” you’re looking for:

Slave men and women appear to have practiced abstinence, often with the intention of denying their master any more human capital." It was not just women who resisted reproduction, in some instances men did also. An ex-slave, Virginia Yarbrough, explained how one slave woman persuaded the man that her master told her to live with to practice abstinence. After three months, the master realized that the couple were not going to produce any children, so he let her live with the man of her choice, and they had children. "By abstaining from sexual intercourse, she was able to resist her master's wishes and live and have children with the man she loved."