Don't check your boots. That's just asking for problems. Carry your boots on. If something happened and they lost your boots you're going to be stuck with rental boots. You don't want that. You can deal with rental skis a lot better than you can rental boots. Carry your boots on.
Anytime I travel with my gear, my boots are one of my carry-ons. No way I'll ever check my boots if I'm planning on skiing while on vacation.
Next semester I'll be studying in Europe...what would any of you recommend I do with my boots/skis..ski bag? Needless to say i'll be on trains all the time...I don't exactly know how they work in terms of luggage..carry on..etc...