In Australia if the rescue is out of bounds it is SES/Police/Fire/Ambulance (I think this is al coordinated by SES?) but they may call on resources such as Ski Patrol.In Japan, basically, all rescue related costs were for free till recently (search & rescue at ski resorts, calling ambulance / fire fighters, etc). Basically, almost all people in the rescue teams are civil servants. In most cases, they are for free (not all cases, though). If somebody gets lost in a ski resort mountain, local police is in charge of the case, however, "time" is important for search & rescue. Police officers are not staying at ski resorts. So, each ski resort has search & rescue team. They are not civil servants, then who will pay for them?. Till recently, many ski resorts didn't charge skiers / snowboarders even if they are rescued when they are skiing / snowboarding OOB. But now, many are charging (it depends on the case, though)
If the rescue is in bounds it is normally Ski Patrol but they will call on SES Plus if required. Evacuation from resort to Hospital, is by Ambulance (who currently a contractor to the State Gov). This might be road or chopper. There is a charge for the Ambulance as it is considered to be post rescue. Normally covered by Health Insurance if you private cover in Australia, if not you can take out Ambulance cover direct with the Ambulance service in most States. Otherwise you might be charged.
I'm not aware of ski resorts charging for rescues, @dawooduck or @Telemark Phat any advice here?