Do not do this!! cabin heat will kill you unless you do not ever ride in the powder snow. it is best to get all the air through and air box, just gut it and open it up to breath! rout it through just behind the windshield and just have a very thin snow filter there. allot more power.
i have built alot of sleds with no airbox and it realy didnt change performance and it cleaned up the engine compartment alot but every mod ive built has had all the underhood insulaition taken out and no gauges(exept for tach mounted on bars)and no sno screening in the hood vents.(ligtening the wedge hood by about 10 POUNDS!)
I cant say I would at all recommend doing what was mentioned above.
Taking the hoses of the carbs and leaving them hanging actually makes the sled richer not leaner. because of what it does to the float bowl pressure.
Also Indy Storm these arent just the Carb vent lines. This sled probably has ACCS. Which is a jetting compensator. You cant just pull the lines off it and throw them down in the belly pan like regular carbs. You HAVE to run an air box with this system. If you eliminate it you need to change the pilot jets, needles and mains to the specs of a sled WITHOUT ACCS. Just gut the stock air box check your wash and adjust from there if you really feel you need to. But it should be fine stock gutting it only has marginal gains anyway.
As for those dumb cone filters... Pulling hot under hood air is never good for performance. And those cone filters even with the prefilter material on them like to suck in snow dust if you get snow under the hood. Thats never good and can lead to a seized up engine. Plus you would have to eliminate your ACCS and buy all new jetting parts to be correct.
Cone filters can also change the air flow enough that the fuel standoff which is present will cause problems. Notice how your airbox is usually kind of oily? that is from the fuel standoff condensing and settling on the airbox. Down draft carbs on older v-8's had the same problem if the air cleaner wasn't tall enough to allow for the stand off.