Honestly, that's what I spend most of my time doing in this game. I can't tell you how many times I've crashed my horse and had to pick the pelt back up off the ground, lol.
Hunting various animals and going after some of the Legendary ones is so much fun. Some of the hunts can actually be pretty epic. I recently tracked the Legendary Moose for about 20 minutes or so. I started tracking it at night, so by the time I was closing in on it, it there was a thick layer of fog rolling in from the lake. Seeing that big monster of a Moose (that thing really is HUGE) coming strolling into a clearing through a thick fog was just epic.
The Legendary hunting trips can really be fun when you're using the actual legendary animal map as opposed to googling the locations. It really gets me immersed into the game.