If your enrolled in AROTC, you won't be going to the USMC Course.
There is a summer and winter Mountain Warfare Course, the best you can do is what Clarkson advised, that to your cadre when your at school and let them know you would be interested. When my son went there was no application process, Two slots showed up at Brigade and the MSgt just happened to see them, he contacted my son and asked if he was interested. Son had about an hour to say yes or no so he could get the slot, it happened that fast.
As Clarkson said it's highly unlikely that you would get a slot, just let them know and if your cadre is one that keeps up on any slot that comes up, and your high enough on the battalion OML you may get lucky, but don't count on it. For now research the things that you do have control over and do those things well, if you do you will give yourself more opportunities as you progress through the program. You will need to be a contracted cadet to be eligible for any of these schools.