I'm all for more animals, but let's go a little more into details.
We have 4 different kinds of animals:
A. Critters: inventory animal, doesn't require fighting (eg. Rabbits)
B. Small animals: inventory animal, requires fighting (eg. Swans)
C. Large animals: liftable animals, requires fighting (eg. Foxes)
D. Huge animals: can't be lifted (eg. Mammoths)
Now let's think what could be added to each.
A. Critters:
Forests are well populated by critters. We have crabs on sandy shores, and we have toads, frogs, and lizards in swamps. We have birds both on land and water.
A good new introduction could be Marmots, for the mountain biome. Some kind of mice could also be introduced, maybe even in the snow biome.
Water, both shallow and deep, could use more life too. Water Turtles could inhabit fresh water and shores, while octopodes could swim in salt water.
Caves could also use some more critters, maybe some other small rodent or similar.
B. Small Animals
This is probably the category that lacks animals the most. Other than adders and swans, I only know of some kind of bird.
A few ideas could include Weasles for snowy biomes, and Minks for swamps. They are both from the same family as otters (but smaller), and both can be found in nordic areas.
Water could use something too, but it would be an animal capable of moving to land, or once killed it would just drop in water and disappear. Sea Turtles could be an option, if we don't care too much for the setting (I mean, we have plenty of things that don't fit). For shallow water only, plenty of small wading birds come to mind.
Even grasslands and forests could use something more here. Some small predator, or slightly larger prey, could work.
C. Large Animals
Luckily we have plenty of these going around on land, from mountain goats to walruses. Only two biomes really lack this category: swamps and deep water.
Alligators have been suggested before for swamps, but more animals could fit in such places. Large snakes could work, but also wading birds like Storks and Herons. Speaking of wading birds, Flamingos could be a fun addition, we already have the crabs to turn them pink!
Speaking of water, we do have many animals that can go there, but none that can't get on land. Sharks are the obvious way to go, since they can be found all over the world, in any climate. Large animals don't necessarily need to be hostile, so Dolphins or even Narwhals could work.
There is another biome that kinda lacks large animals: caves. I said 'kinda' because you can find them, but it's very unlikely to see any roaming around in actual caves; most get either mined out, spawn on lower levels only, or pop out when u pick those weird lamp-stalks in the water.
(Mountain Lions and Black Bears, as suggested by OP, would fit in this category)
D. Huge Animals
Here we have lots of choices, and I do believe it's also the category that can work the most with fiction, being haven a game with magic after all.
I would LOVE to see Big Foot in the forest or a Yeti on the mountain top. Maybe a Swamp Monster!
Being more realistic, we could have more huge aquatic animals, like orcas or giant squid, but also more prehistoric animals like the mammoth we already have (Wooly Rhino and Giant Deer when?).
There are plenty more options, these are just some suggestions.
In the end, any new animal would be greatly appreciated, especially if they lead to new craftable equipment or other recipes.