It's very dependent on your character. A fast character has a much easier time chasing down an elk than a slow one, since the fast character gives the elk much less time to recover between bouts of fleeing. It also depends heavily on the terrain and character tracking skills, as open terrain with clear footprints allows the character to chase the elk a lot easier than in spruce infested forests where you have to get very close to the elk before it notices you and flees (and so it has a lot more time to recover), in particular if you can't always follow the footprints, as trees are in the way of the ones you could see.
However, something that HAS changed is that snow now affects others than the PC, in particular deep snow with a crust strong enough to carry the PC, but not strong enough to carry the elk. That situation is drastically different from before the change.