With a Polar Bear, I'm looking for something more playful and fun. I've got a couple of ideas, but I don't want to restrict someone's ideas, which may be much better than mine.
Although I like your #10 entry, it might be better if the Christmas tree and lights were removed, and the Snowman and kids bigger. I would also prefer darker blue outline on the "Ho Ho Snow" lettering (like on your #3 logo), and the middle of the letters whiter.
As I've been looking at the different logos, I'm thinking that simpler designs with fewer elements may be better.