Bears, at least nowadays, are not afraid of campfire at all. In fact it may attract them, because they think that either people will give them food, or that they will scare the people off and help themselves. This happens even if areas where bears are hunted (maybe because most hunters don't hunt bears anyway). But I have no idea how it could have worked in ancient Finland... Were there free buffets hikers?
Small animals used to humans are also not afraid of campfire, which suggest they are able to discern forest wildfire from campfire (like raccoons or feral dogs), though they may be afraid of people themselves (easily visible when near fire).
As for wolves, they avoid humans, so campfire may deter them, but only because they will associate it with humans. They learn quickly though, and stop being afraid if something isn't hurting them. Being near a campfire doesn't hurt, so...
Game animals may be more afraid of fire in general, but I still think it would be more thanks to association with human (i.e. predator) than with small fire. They do run away from big forest fire, actually from smoke even, but this is also dangerous for players in the game.