This was possible at least in North Europe. Hunting as a means of subsistence was widely practiced especially in the eastern parts of the Kingdom of Sweden (the region that is Finland today) and most likely similarly in North Sweden and Norway. Long winters forced peasants to find alternative ways to support themselves and hunting was one such way in most inland regions (seal hunting and fishing had a similar role in coastal areas).

Since there were few people and much land, this did not usually collide with the interest of the crown or noble families - quite to the contrary, peasants were taxed also for the game and furs, and therefore the ruling class benefited from hunting as well without having to roam the vast wilderness themselves (except for leisure purposes).

The winter hunting was actually a very spectacular feat: men of the families left for the woods for extensive hunting journeys, some of them staying away from their families and living in the woods for months in a row. Some even had semi-permanent winter settlements or cabins in the game-rich wilderness to serve as outposts. The demand for winter furs all over the rest of Europe was very high and therefore fur trade was an important means of livelihood for many northern inland peasants and full-time hunters.

Hunting took place also during the summer, but to a lesser extent. Fishing was similarly important, although fish was more a direct food source and less a trade good. Needless to say that even though these goods were taxed by the crown, the peasants (especially the Finns living in remote locations) were happy to avoid any taxes they could and therefore collecting them was often very inefficient and difficult. There were people who completely lived off the wilderness and perhaps never paid any taxes for their catch.

Sources: Lappalainen, Mirkka: Jumalan vihan ruoska; Huurre, Matti: 9000 vuotta Suomen esihistoriaa. (Both are in Finnish; the latter book is actually about the prehistoric times, but covers the Iron Age/early Middle Ages as well, since they are typically considered to be prehistory in Finland)