I would not recomend using anything but a DOT approved helmet. This is your brain you are trying to protect. Injure it and you are done!
Ski helmets will not do the job.
The only advantage to Carbon helmets is the are lighter... If you got the cash hey why not.
I have been using my motocross helmets for Skiing, Downhill mountain biking and Snowmobiling for a couple of years since I destroyed an approved full face bicycle helmet while downhilling. Doctors could not believe I survived. my neck never gets tired, My head definatley is hot in the summer but perfect in the winter.