Just be aware that between Christmas and New Year is the single most expensive time to ski in the Alps. almost everyone in Europe gets that week off and a lot more Europeans ski than Americans. I go every other year, usually late January.
But it is not too complicated. Pick a place, book lodging, buy an airline ticket, see how to get from the arrival airport to the resort (usually fairly easy by bus or train). Then pack your ski gear and go. It really is not much different than skiing in the US, just a longer airline flight. and it will be refreshing to see how much lower lift prices are these days compared to the US.
BTW, Switzerland will be noticeably more expensive than France or Italy.