Alright guys, here are some suggestions for this project:

Tilesets

Feel free to use any winter tileset. Here are some suggestions:
-"Holiday Hare Fix v2" by Feaw. It contains 5 different (and improved) versions of the official HH tileset and 2 variations.
-"Xmas Carrotus" by Bluespaz07. It's not exactly "Xmas" themed as the title states, however it's a fine winter recolor of Carrotus.
-"JJ1 Holidaius". It contains 3 variations of the Holidaius tileset from the original Jazz Jackrabbit.
-"CandionV". Some may consider it too hard to look at due to the bright colors but that could be easily solved with a color palette alteration. Except for that, it's a very good looking tileset.

These are the ones I feel like they would work the best. Feel free to find and suggest other tilesets.

Music

Luckily, both JJ and JJ2 have Christmas OSTs so this shouldn't be a problem. Probably most other video game winter/Christmas themed songs work as well. I suggest using Jaseke's remake of Winter Hare. Sounds sick!

Scripting shenanigans

XxMoNsTeR offered to help with scripting this level pack. However, ideas for what to implement are still needed. All of the ideas so far:

Monster's idea: Being able to disguise as a snowman. While under disguise, enemies can neither track nor hurt you.
My idea: Collecting presents instead of coins, which can be used to purchase all sorts of upgrades in mid-level. Upgrades can include weapon upgrades (and ammo), jump height, firing rate (if rapid fire drops are removed), health etc.
cooba's idea: Crates with random contents. Kind of like presents in real life: It's a mystery!

Please mention your thoughts about these ideas, whether you would like to see them happen or not, what could be improved/changed etc. along with your own ideas.

Other ideas & suggestions

-"Blizzard Peak" by PT32 has a good looking blizzard effect to it. This effect could look great in one of the HH17 levels.
-Water might work if it's "freezing water" that damages you.