This movie is from the 90's or early 2000. A little bear is tamed and lives with a family. The authorities want to take the bear, but the family don't want to give it up. I know the whole movie took place in the winter.

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The Bear is a possibility

Sounds like Ms. Bear. (http://www.imdb.com/title/tt0119724/reference)

Thanks Quinn F

You're welcome.