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!