Some things that would make it hard for animals that normally live in the tundra to live in a different biome would be that they do have thick hair and some have blubber so they would over heat. Also the animals mostly eat fish and animlas that live in the ocean.
Adaptations: Animals need to have thick fur and some bulbber so that they can stay warm in the frozen tundra. Plants need to have short roots because the ground is frozen and the further down you get the colder the ground gets and the plants can't get their roots to grow through.
If you put the animals that live in the forest into a different Biome they would probably be able to survive but not for very long, most have warm coats and live in the cold and warm months of the year so they could find something to live off of for a while.
Adaptations: Animals have adapted because they are able to eat berries only some of the year becasue the snow and becaue they don't grow year round. Instead of eating berries, when there is snow they will eat tree bark. Most animals that eat berries hibernate so they will eat a lot of food and then they will sleep all winter or most of the winter.