The ski resorts hire people to do "Ski Patrol" and many of them are EMT (or even MUCH higher) certified. It can be very seasonal work... Sometimes they're a volunteer group that's affiliated with the resort. They can do either.
The Dodge Ridge Ski Patrol is an example of this and they have their own website... http://www.dodgeridgensp.org/
No, I'm not a "Patroller" with them... or any other group.
Yes, most do, and its a great job, I worked a few winters at a pennsylvania ski resort, they required Basic level certs then trained you up to their standards. Go to the national ski patrol website to see what they can do.
The Dodge Ridge Ski Patrol is an example of this and they have their own website... http://www.dodgeridgensp.org/