as far as I know, the Swedish top slopestylers get funding from the Swedish Olympic Committees (SOK) talent and developement programme, and that could be anything like help with camps, travel costs and physicians. from what I've heard it's pretty tailored, i.e. Henrik Harlaut can get a different type of backing than Jesper Tjäder - it depends on what the respective athletes are asking for.
i have no idea how it works in other countries.
also - the SOK is not entirely tied to the Swedish Freeski Team - there are guys on the team that doesn't recieve funding from SOK at the moment. most of the A team does though and I know a few of those who doesn't are in the talks for the future.