Remember that you are reading a newsrag. Yes, they can do that except for the trespass issue.
66.0409 Local regulation of firearms.
(2) Except as provided in subs. (3) and (4), no political subdivision
may enact an ordinance or adopt a resolution that regulates
the sale, purchase, purchase delay, transfer, ownership, use, keeping,
possession, bearing, transportation, licensing, permitting,
registration or taxation of any firearm or part of a firearm, including
ammunition and reloader components, unless the ordinance or
resolution is the same as or similar to, and no more stringent than,
a state statute.
Stringent synonyms, strict, binding strongly, making strict requirements, restrictive, severe.
Trespass, with or without arms, requires effective notice not provided (certainly in other jurisdictions) by mere signage.