Most towns in NH do not allow mobile homes on private property unless they've been grandfathered in. They must be in a designated mobile home park. My town allows a temporary mobile home to be set up for a period of one year during CONSTRUCTION of a new home.
It varies by town and the zoning laws change every year.
Grafton appears to be where Free Staters like to park their mobile homes. There are no zoning prohibitions in that town.
OTOH - towns like Hillsboro will not allow trailers in the historic district, the commercial district or the 100 year flood plain. Other towns may not allow them at all. Some allow parks with a specified number of units.
Even if your town has restrictions, you can appeal the zoning laws. Local laws must comply with state and federal rules.
New Hampshire Town And City