I have caught 3-4 kuikka this warm season in snares set at the water's edge (river). That's 4 traps set a few steps apart. Initially, they were baited with fresh lingonberries. The berries have gone stale but the kuikka have still been taken in the traps, WITHOUT eating the bait. So, it's possible they are simply stumbling into the traps randomly.
In the very early game, I used the free handfuls of seeds given by the missions to bait snares, successfully. Again, the bait was NOT eaten by the catch. It may be that seeds cannot be consumed by animals? Anyway, SOME seeds seemed to work while others never caught anything, so, again, it may have been totally random stumbling into traps. In fact, early on I have set snares with NO bait at all and had good success in places with a lot of bird activity.
For hares, turnips are so successful in my snares that I stopped trying mushrooms (which never caught anything). Also, I bait heavy deadfalls with turnips and have caught many deer/elk in them.
When I see owls and hunting birds, I bait with raw meat and have had good success.
Regarding the traps, almost all my bird catches have been in snares. Only rarely have I had a bird caught in a paw board trap. Likewise, only rarely have I caught a hare in a paw board trap.