The Alchemist infusion frost bomb with the alchemical items that do ice stuff (I believe there is one where you pour a liquid out onto water and it flash freezes) would probably do the asthetic you describe best.
I am big advocate of Kineticts though and a water Kineticts with a cold Blast could do what you're are after and they can be really fun in melee and range.
With snowball I think the Eldritch archer Magus archetype might be of interest to you.
Frost bomb discovery would make good snowballs. In a home game, I'd probably let you have that at first level and require a separate discovery if you wanted the fire bombs back.
Normally I'm not a huge fan of multiclassing just to multiclass, but in this case I might take one level of witch with the winter witch archetype to give you snowball on your spell list (which would also let you use snowball wands) as well as some decent other cold theme powers and flavor.
I would definitely choose alchemist for the main class though. I would be tempted to take the grenadier archetype (mostly because I like it a lot) and use then I could shoot liquid ice with my ranged weapon. Having a snowball thrower is cool.
Grenadier just makes being a bomber a bit more streamlined.
A treesinger druid could get a puffball companion - a flying fungus which might look a lot like smoking icecream.
Also it's called a puffball which is a plus.
Don't forget about straight arcane caster with customized spell creation. Just think of all the kinds of spell-creation fun you can have here.
