Marriage for love was not completely unheard of.

With those not of noble birth, typically the gains of a planned marriage would be minimal. So peasants, merchants, would very much have freedom to follow their hearts.

In regards to nobles, it depends. If you're a first born child, it's likely all that responsibility would make the prospect of love marriage out of reach. But later born children wouldn't have as many confining responsibilities, and would more likely end up marrying for love

It's a misconception that young people in the medieval period were married off as children. While this was sometimes true for nobility, among the lower classes and particularly the rural dwellers, this was not really true. In England at least, it would not uncommon for a woman to reach her twenties before marrying. A daughter was not exactly the worst thing to keep around the house to assist with chores.

The largest barrier to finding love for a 'peasant' was that, relative to today's urban youth, the number of suitors you had wasn't necessarily that big. There's no doubt that, at least among the urban dwellers, property and 'means' were an important factor to the reasoning behind men and women waiting until they were older to get married. No woman would want to marry a man with no prospects (at least, rationally) nor would a father acquiesce to such a union (unless he was perhaps a mixture of soft and daft). So, if you were a young man or young woman, finding the right match was mostly a matter restricted not by arrangement, but largely geography. An urban dwelling man or woman would have more options, but a young woman was unlikely to venture far from the estate her family worked to socialize or marry. One might expect that children of a suitable age would engage in wider ranging socialization at fairs and the like, as continues to be common in rural areas today, but anyone who grew up rurally and stayed there knows that your choices are often very limited. On the other hand, anyone with experience with arranged marriages also knows that love can be found even in situations of conviencence.

If you're interested more in Medieval marriage, this book was good, although again, only focuses on England: http://www.jstor.org/stable/10.7722/j.ctt81hjf

One thing not mentioned already is matchmaking. These would be local women interested in setting up a good marriage, both by personality and economics. How this was practiced of course varied by community and how much the singles wanted to object or interject to proceedings. R/Judaism might have someone who could talk about what the shidduch practice was like at that point and whether anyone compared of contrasted it to the practices of the Eastern European (or Andalusian) neighbors.