Film permits: Shooting in public is free
The "freedom to roam" act allows for easy permit processes when filming outdoors. In general local police and municipalities are very cooperative, and local mayors - and citizens - are rolling out red carpets rather than red tape when welcoming film shoots to their municipalities.
On a general basis it is not a problem to close roads, you are often met with willingness from local municipalities and police, and often you can have your own traffic control. However, this depends on which area you are shooting in.
Filming on private property requires a permit either from the owner or from city authorities. A permit from the police is needed if the filming requires special traffic arrangements (i.e. re-routing or stopping traffic).
Regulations apply for motorized transport (helicopter, snow cats, snow mobiles et.c.) in the wilderness, mountains and national park areas. Allow for some planning time to work out logistics with a line producer or location manager who knows the area. Applications are sent directly to the respective municipalities, and/or to the national parks.