Answer: I can find nothing in the state statutes specifically regulating the installation of air conditioning units in park homes or privately-owned homes. It is correct that some landlords forbid them to be installed in rental homes, presumably because of potential damage to the interior or exterior during installation; plus, there is the risk of a poorly installed unit falling on someone.
However, if you own your own home, I see no problems. I've never seen anything in any rules placing limitations on the installation of AC window units, and don't expect to. Subject to reasonable limitations on installation, andcompliance with applicable building and electrical codes, I don't see any issues.
Placing such limitations on residents would probably trigger an onslaught of "reasonable accommodation" requests, since many older people who are home-bound or in need of air conditioning during hot spells - even in Oregon - and for obvious health reasons, should be able to have it.
The only landlord issue I can see with window-installed ACs is appearance from the outside. If a unit is inoperable it should be removed before it becomes an eyesore. Subject to a landlord's reasonable limitations on placement (like satellite dishes), there are no other limitations that I'm aware of regarding installation of these units. I do suggest, however, before installing one, check with the manager just to make sure there are not issues you may have overlooked - especially concerning proper installation.