This is actually a really difficult question to answer. The problem we have is that our primary sources for the First Crusade don't really talk about the practicalities of arms and armour all that much. Even the Gesta Francorum, which is the most military focused of the eyewitness accounts, makes only minor mentions of armour in its text. You can actually see this for yourself if you'd like. Deremilitari.org, which is an excellent site when it comes to medieval military history, has an account of the First Crusade made of sections from various major contemporary chronicles. It's not the best composite text (there's an amazing Penguin edition) but it's enough to give you the idea and it's free.

So, without a lot of primary material to work with we're sort of left with secondary material and speculation. Speculation is satisfying but also very limited in its value while secondary material often only provides really vague details. For example, we know that members of the knightly classes, who were also by far the most likely to have owned proper armour, would have had horses so they would not have had to march while wearing their armour making it a much more practical option. However, most of the horses on the First Crusade died pretty early on in the campaign, and the few that lived often had to be preserved in good condition, so this really limited this option. The threat to Crusaders was also not as omnipresent as we might suppose. Scouts would have enabled some tracking of enemy movements and certain areas would have been difficult to launch ambushes/attacks from, meaning that Crusaders could have only worn their armour at certain times when the threat of attack was high. Again , though, our sources don't say much about this so we are forced to impose our own expectations and theories onto a limited amount of evidence.

In his recent book How To Plan a Crusade Chris Tyerman has argued that Crusader warfare wasn't all that different from much of contemporary European warfare. With this in mind, he draws evidence from elsewhere in Europe to argue about the logistics and practicalities of Crusade. It is a testament to just how little we know about the practicalities of day to day campaigning that he barely mentions this topic at all in his entire book. The one bit of evidence he does point to comes to us from that endlessly valuable, if tricky to interpret, source: The Bayeux Tapestry. The Bayeux Tapestry does not just include famous scenes of the Battle of Hastings, it also includes at least one other campaign as well as the logistics involved in the conquest of England. One scene features troops carrying arms and armour in a wagon train. While the evidence is limited, there is reason to believe that this would have been standard practice for medieval armies. However, whether Crusaders would have followed standard practice, no matter what Tyerman argues, is hard to prove especially with regard to their own safety. While there was something approximating rules to the structure of medieval battles in Europe, there is no reason that the Crusaders would necessarily have expected those rules to apply to war in the East.

In the end there's very little we can say with certainty, but the most plausible explanation seems to be that armour would have been mostly carried as part of the supply train or within the retinue of the knights in question, but probably would have been worn in circumstances when battle was expected or seemed likely.

Chris Tyerman's How to Plan a Crusade includes a lot of detail on the logistics and practicalities of Crusades in general, but is a really dense book and definitely not a great introduction to the subject.

Thomas Asbridge's The Crusades is a much better starting point for all things Crusader history related.

I'll add to /u/Valkine's point that "we don't really know" with what the crusade chronicles seem to obscure.

There are actually quite a few references to knights donning their armor right before a battle. The question is, does this reflect actual practice or a literary topos--is it a verbal cue to say, "They were ready for battle." When we look at the romances, which are set in Europe, we don't hear about knights wearing armor to travel. What we do read is that immediately upon arrival at a castle, they remove their armour. Does this reflect travel practice, or is it a literary trope to signal the passage from danger (abroad) to safety (hospitality of a castle)?

There is one explicit reference that I'm aware of, to crusader knights and armor while traveling. It's from the Gesta Francorum. I'll quote it here because it's, well, ambiguous:

We who had stayed at Coxon set out and began to cross a damnable mountain, which was so high and steep that none of our men would overtake another on the mountain path. Horses fell over the precipice, and one beast of burden dragged another down. As for the knights, they stood about in a great state of gloom, wringing their hands because they were so frightened and miserable, not knowing what to do with themselves and their armor, and offering to sell their shields, valuable breastpieces and helmets for...any price they could get. Those who could not find a buyer threw their arms away and moved on.

So basically, it could support either interpretation. Or it could be a literary trope reflecting their overall incapacity (wringing their hands helplessly => no armor). I'm inclined to suggest it means that in this case, the armor was on the beasts of burden. (horses, oxen...Fulcher of Chartres talks about crusaders buying dogs and goats to try to make up for the loss of the pack animals). The knights watched other people's armor go off the cliff with the horses :( and would rather get firesale price rate instead of nothing.

Here's a fuller excerpt on Google Books.

Would they even have armor? I assumed they were just "conscripted" and given a sword and armor was either scavenged off the dead or earned later.

I'm being downvoted, but that wasn't a comment or snark. I legitimately was asking if they would have armor. I assumed most armies back then were conscripted of peasants.