haha i used to love that game

I havnt played it in years.
I like the concept of your remake. Polar bears are definitely cuter than some dude on skis xD. Withthat said there are some points i feel could so with some improvement

I've made a really quick edit and squared the spots i changed

1.The palette! Although your palette isnt -bad-, it could use some livening up. Your colours are quite close together leaving some details to look sort of washed out. It also seems like a happy cutesy sort of game so why not go for brighter happier colours?
2.Depth. You're using darker outlines around the edges not giving thought to the depth of what it is you are outlining. For example, the polar bear. The head is closer to us in this view than it's bum, yet the bum has more emphases due to the darker outline. The head sort of fades/melds into whats behind it. Why not try adding a darker outline around the head to draw the eye there first? This same problem is occurring with the ski jump. The darker outline should be placed to define the object from that which is behind itself.
3.Redundant colours. Theres just one, but its there haha xD. The flag had two reds that are so close together that one of them is really not needed at all. Try replacing it with one of the darker greeny blues you've used to outline other things.
4.Jaggies. You've left some weird jaggies around the bushes and stump. The 1-3-4 pixel line on the bush is making it look a little weird. you can fix this by either changing it to 1-2-4, or just adding in some simple a/a. The stump you can fix by changing the top from 2-6-2, to 1-8-1 or again just using some simple a/a.
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The title screen i think is going to look really nice

. I love pixelled snow scenes haha
a few suggestions and again an edit

1.The top of the igloo seems to be at a different angle than the door. We should technically be able to see more of the 'circle' at the top.
2. You've made the bg and trees look as if it is a low light setting..night or overcast perhaps but your snow is crisp and white like on a bright day. I suggest changing the colours of the trees+sky to match that.