Air cleaners???

Welcome to the forum! In regards to your question, I'd suggest looking at K&N's website here:

http://www.knfilters.com/universal/universal.htm

This will give you all sorts of options in regards to what style of filter, and from there it will give you every dimension of the air filter. I'd imagine getting the biggest filter possible will lessen the effects of having an air filter on there. The K&N's aren't very restrictive to begin with which some guys in the dirt powersports arena avoid them, but being in the snow and just wanting something to keep the dust out, K&N's would be a great idea. You may want to consider building a bracket to hold the air filters up so that they don't make the carb boots sag with the air filters hanging off the back. I don't know whether its an issue or not, but something to consider.

Another thing that I have heard is that with just the carbs hanging out like that, they actually suck hotter air than they would if it had an airbox that sucks air from the top of the hood. At any rate, good looking sled, see ya on the trails!

I put a 700 in a xlt we used a 700 air box and trimmed it for the steering post I have an air box

I would definitely get an air box so you can pull cold air from behind the windshield. The 99 RMK set up would work good for you. The problem as mentioned previously is that you suck in a lot of hot air with no air box. One more thing is that with no air box the under hood barometric pressure varies tremendously with speed so the thing is almost impossible to jet properly. I tried pod filters once and threw them away.

I would sell you an air box for 25 plus freight