This is obviously a very broad question, and not one that can be answered simply or completely satisfactorily, but I believe I can help with a momentary picture, if nothing else. But before that, let me outline some of the fundamental problems in answering such a question, and why no answer to it can be taken as gospel:

First of all, there is the obvious problem that 'medieval peasant' denotes millions of people over hundreds of years, stretching across hundreds of states and climates. There's going to be a gigantic difference between what life is like for a 'medieval peasant' living in 6th century Sicily and 14th century Denmark. In certain places, times and climates, people were starving, murdered by conquering armies and oppressed by local lords. In others, food was plentiful, the weather was mild, and warring nobles was something that happened far away and wasn't to be worried about.

Secondly, there's the problem of conceptions of 'happiness'. People, in all places and times, certainly had an idea about what 'happiness' was, but would it be comparable to what we think of as 'happiness'? Even today, we would have quite a lot of trouble defining the word. If, for example, we define 'happiness' through a modern, liberal capitalist perception, as something denoting professional succes, wealth and being 'upwards-moving', then most medieval peasants would certainly not recognize themselves as 'happy', being pretty much stuck where they were. We could also define it through the idea of contentedness, being more or less satisfied with ones place in the world and ones personal and material surroundings, in which case a lot of peasants would most likely understand themselves as 'happy'. Then there's the religious angle, which most of us, today, would probably have a hard time grasping properly; happiness could also mean feeling sure of ones piousness and future place among the righteous in heaven.

Lastly, there's the problem of sources. With literacy being as rare as it was throughout all of the Middle Ages, peasants writing about themselves and their lives was rare enough to be virtually non-existent in our extant source material. Adding to this the fact that scholars of the time were rarely very interested in the thoughts of lowly peasants, we just don't have much material to analyze. What we do have are the sources produced by the church, but it should come as no surprise that these generally don't focus on the 'happiness' of the locals as much as their piousness.

But!

Through a rather convoluted and unrelated series of dramatic events, we do have one unparalleled work of medieval anthropology, which lends us an infinitely fascinating view into the intimate, emotional, material and social lives of a small group of peasants: The Inquisitorial Register of one Jacques Fornier!

See, between the 12th and 14th centuries, the Church had a bit of a problem brewing in parts of France, Germany and Italy; namely, the uncontrolled spread of the greatest heresy anyone had known since the first centuries CE - one so terrifying that it was not only named 'The Great Heresy', not only seen as a true and credible threat to the unity of the Roman Church, but became the originator of the word for heresy in several languages: Catharism! I won't get too much into its theology and history, but in summary, it was a neo-Gnostic ascetic movement that had most likely arrived in Western Europe through communication with the Bulgarian and Byzantine Bogomils - but that's a heresy for another day.

Anyways, after more than a century of fighting Catharism with anything from theological debates to an actual Crusade, its evils lived on. And then, an enterprising young bishop of the Southern French town of Pamiers took matters into his own hands. Jacques Fornier, who would later become Pope Benedict XII, conducted seven years of meticulous interviews with the local villagers from 1318 to 1325, trying to weed out heretics, writing down their words almost verbatim, conducting follow-up interviews, cross-interviewing family members, friends and enemies, the works. And because of his tireless hunt for heretics, we have perhaps the single most detailed and reliable source for the lives of medieval peasants (of a certain, short period, in a certain, small area) in history.

And so, to finally answer your question: yes, some peasants certainly saw themselves as happy. Like Pierre Maury, the shepherd, who scorned material wealth and the villagers obsession with family and hearth, and was happy to own only what he could carry on his back; though he often missed the embrace of a wife. Quoting here from Le Roy Ladurie's stunningly fantastic work, Montaillou, which is also the primary source for this answer and a book I cannot recommend enough*: ''*Well shod for his long journeys in a pair of good shoes of Spanish leather - the only luxury he allowed himself - detached from the goods of this world, careless of the almost inevitable certainty of being arrested at some time by the Inquisition, leading a life that was both passionate and passionately interesting, Pierre· Maury was a happy shepherd.''

More than anything, though, we learn from these sources that happiness in this tiny village was generally understood in much the same way we understand it today: as something that comes and goes. There were happy years and unhappy ones, happy marriages and unhappy ones, and some people were prone to happiness, while others were prone to misery.

In this vein, I think the most important point to make about your question is that peasants lived sometimes long, sometimes varied and sometimes happy lives, though their material and social conditions (as well as expectations) were certainly very different from ours - but a poor life can be a happy one, just as a rich one can be miserable, and they knew this as well as we do.