Rather than a horse, it would be more likely they would own an *ox. Or, rather, as has been pointed out, that they would own some share or portion of said animal.
A peasant's life has been unduly portrayed as endlessly depressing in fiction. The average peasant, presuming they **survived to adulthood, would be far more likely to die of old age than anything else; at a ripe old age of 70 to 75. Furthermore, there were a number of ^feasts, ^festivities, and ^games each year. Nor would a typical peasant wear muddy greys and browns. Certain dyes were reserved for royalty and the rich; but plenty of dyes weren't, and ^^embroidery was a well-known and widely-practised art. People didn't always bath often, but that was because, while you could argue that dirt made you more likely to get sick, everyone knew that freezing in the wintertime made it more likely for you to get dead. And you needed that firewood to keep your house warm. In the summertime, there were streams and rivers if you wanted to get the sweat and dirt off, which people would regularly take advantage of.
* A domestic bull, raised and bred for work rather than food, and possibly gelded. The plural is "oxen", not "oxes"; a statement which also occurs in a famous silly poem about English spelling. And at this point, there may be approximately two and a half items of TMI, and here we have one proverbial lampshade.
** The major problem here being surviving childhood illnesses long enough to develop a robust immune system; so, if one made it to about twelve, one was most likely "in the clear".
^ A typical use for a feast would be to get rid of all the food that was closing in on its due date. That being said, smoked and salted meat can keep for a long time, and it is most likely proper to regard with dubiousness any claim that medieval people regularly ate rotten meat. The average peasant used about 45 kg of salt per year, far more than would be needed for table salt. Festivities would generally occur on holy days and various other events people felt like commemorating, such as marriages and historical events. Games included various forms of ball-and-goal played against nearby villages, and were typically quite brutal. To the point that the Catholic Church made particular appeals to keep the violence down and enacted limited bans; the most notorious other such appeals being
jousting and the
use of crossbows.
^^ If, at any point, you enter a fantasy or medieval world and desire to sell your clothes off, do not expect the locals to be that impressed with your factory-made clothes. Yes, the threads are quite densely packed...On some clothes. However, the dye job is most likely one that will quickly flake away; the clothes themselves are relatively thin; and the embroidery is non-existent. You would be much better off selling the idea of a zipper...Carefully. Accidents can happen. A factory means you can pay for a new shirt with the equivalent of two good meals at an "inn"... It also means you still get what you pay for. My apologies for any upset.
ps: ...And my apologies for the info-dump; it seemed useful to address some info around the general idea of peasant livelyhood and welfare.
