The sentence "Bears sleep through winter in a den" is grammatically correct! Let's break it down:
- Bears is the subject (who we're talking about).
- sleep is the verb (what they do).
- through winter tells us when they sleep (during the winter).
- in a den tells us where they sleep (inside a cozy place called a den).
So, the sentence means that bears rest all winter inside their dens.
If you want, you could also say: "Bears sleep all through the winter in their dens." But your sentence is perfectly fine as it is!