Everyone say do not wear cotton as a base layer because the cotton retain the moisure. But i think, at least in Northeast, most of time you won't even sweat. It is just too cold and unless you kept in the black or double diamond, i don't see much chance to sweat at all in the 20-30 degree temp most of the time.
I address my kids including myself a cotton (maynot be 100%) turtle neck, a wool sweater, and a ski jacket on the top; a cotton bottom (I bought from China), or a basic layer bottom bought from the store here.
The coldest part typically is your face, and ears; possible hands and feet. For the face and ears, you need a fact protection -- any ski store will sell it, for the hands/feet, other than good mitten and wool ski socks, the only thing really help is the hand warmer and feet warmer.
Only when you don't feel cold, then you will enjoy the ski -- it is a super sports and hope your kids will love it as my kids do. :-)