Ski areas around here (CA) are both private and public. There are even
some laws preventing you from leaving a private resort to
head off into unpatroled land at some, not all of them.

The Sheriff's Dept is in charge of SAR here, and can bill for
costs. However, unless there is criminality involved, the real boneheads who bring it on themselves are reminded they can donate to the SAR organizations. The often do, having realized their goof,
and being grateful for the help. Some come to the meetings to say
thanks, some send a check for anywhere from $25.00 to $10,000.00
or more. All in all it is a pretty good system. A good portion
of the funds and volunteer time go to education to help prevent
searches. Since instituting the educational portion of the local
nordic SAR team in 1970, there have been NO searches for lost
kids who have been through the 4th grade survival/staying found
school trainings.

The majority of the costs born by taxpayers are for the coordination
by the Deputies of the search, and for some of any helicopters
used. Often the helicopters are military and are paid for
through their training funds, i.e. they would be out flying
around anyway.