All of the birds in the game right now are birds that are good for hunting or foraging. That makes sense, since a good part of the game centers around doing those activities.
However, something I enjoy in UrW is just the feeling of wandering in the wilderness, so I think I'd also enjoy seeing birds that aren't what you'd call "useful" to me as a player, but would add to the ambience of the game, such as songbirds. So lets say I wake up at my cabin for a day of fishing, and there's a warbler on my fence singing. Or its just finished raining, and because the ground is muddy, there are birds out looking for worms. And because different birds have different distributions in Finland, I'm guessing that you'd be able to tell what region you were in just by what birds were around and what songs they were singing.
While all of this is probably something that could be done with ambient sounds, too, I think it would add to the game to be able to see them. Besides just the enjoyment of the visual aspect of seeing the songbirds, it would also make it seem less like everything that's in the game is just there as a matter of instrumentalism, as a means to an end, so you could feel like you were in a living breathing world. They would naturally also be more common than game birds, and more commonly keep that sense of a living world in your game experience.
Of course, I wouldn't necessarily expect a small songbird passing by to pause tasks the way the game normally does when animals come into your view. Since they'd be there more for the ambience, the game could assume you'd ignore them.
They would also be prey I assume for predatory birds like owls and goshawks, and you could see them being caught.
I assume there would also be a lot of other small animals, like snakes and toads and field mice and so on, that would be between tall grass or lake reeds or sedge, and would have the same purpose. (And of course these have had a role in magic lore, so they might have that added use).