Sure, here are a few of my thoughts how to improve/expand the game (without any claim to be good).

The camera view is a nice artistic style, but also a challenge to the player:

•  I would try to improve the situational awareness (i.e. where the player position is relative to other game objects) with some subtle visual indication of "lanes".
• The controls should feel more intuitive and precise. So I would align the axis of the controller with the coordinate system of the screen (not with the 3d world one), so UP would mean straight up the screen (not diagonal, i.e. forward in the 3d scene). Btw. did you notice that the controls are mapped differently in the menu screen than during the game? =)
• To add some "juice", I would experiment with some dynamic camera zooming/following w.r.t. to the player position. And a screen shake when a collision happens!

You are basically mixing a racer with a shoot 'em up, so I would take inspiration from those kind of games:

• The game is currently very unforgiving. Maybe give the player a health bar or a number of lives, so that the game is not instantly over after a single hit? I wouldn't interrupt the game either, just show some visual effect and reduce a life. Let the race go on. And make the player invincible for a short period of time.
• I would try to come up with some interesting obstacles (e.g. reindeer, tree trunks, stones, or ditches) that also need to be avoided. Icy or snow-free patches could also be fun if they change the control behaviour a bit. Last but not least, what about jumping? Maybe the player can avoid some obstacles or the fallen enemies with a timely hop.
• Powerups would multiply the fun for me. I would come up with my own variants of shells, stars, bananas, etc. from Super Mario Kart or similar. This is naturally the place where you can have fun with visual effects the most.

You have currently three goal conditions in the game:

• I don't feel that this is beneficial. One single obious goal might work better. Say you start at the last position X and need to "overtake" (i.e. get rid off) all of them to win the race.
• Levels! Start with a short race (a few dumb enemies, no obstacles or powerups) and then increase the difficulty gradually. Introduce a new enemy type, obstacle or powerup every other level or so.

Sorry, this got longer than planned ... I like brainstorming about stuff like that =)