The Middle Ages is a fairly broad time period, but your average 'working the field' peasant would definitely see artwork, though it would generally be in church. Mass was performed in Latin and most peasants (at least in England and Ireland) didn't speak it, so a lot of religious instruction was done through art and theatre (look up the York Mystery Cycle for a famous theatrical example). Religious art was predominantly in the local church in the form of stained glass windows, sculptures, painted miniatures, frescos, and - of course - illuminated bibles which would be displayed on altars. These bibles could be excessively ornate with gold and jewel encrusted enclosures, and richly painted and gilded pages. The Book of Kells is the most famous Irish illuminated bible I can think of, but there's literally hundreds of surviving examples.

Richer folk would have a Book of Hours made for them. These were prayer books and even more picture heavy. The majority of illuminated manuscripts you find for sale in auction houses are these.

Returning to peasants and the question of oil paintings... there weren't really public museums or galleries where people could enjoy art in the same way we would at the Tate or Crawford. If there wasn't oil paintings in their church, the only place they'd see them would be in government buildings or a rich persons home, and the likelihood of that depends on when in the Middle Ages you're talking about. Miniatures would generally be more common than giant, Caravaggio style paintings, though the closer you get to the English Renaissance period, the more common paintings and printed artworks become.

Don't forget, people could and did create their own art. They just wouldn't have had the access to things like vellum and lapis lazuli the same way monks and nuns would have. In fact, for vernacular medical manuscripts like Harley 585, an Old English leechbook, you'll notice the vellum used is of a much inferior quality to any used in a bible and there's way less ornamentation and colour (though the scribe draws a little snake next to every mention of one which I personally love).

So art in general - yes. Oil paintings on canvas - less frequently but not impossible.