Some HOA have a "commercial lot" where the residents with boats, enclosed trailers, jet ski, or anything else such as camper or motor home can park their legally registered and insured vehicle.
I don't see why you couldn't park your large horse trailer alongside these other vehicle...
Or, park at a storage facility that has high fences and security gates.
Lock your trailer, check on it and its insides occasionally and make sure the hitch is blocked/locked and secured...
Of course, insurance is a must no matter where you keep such a vehicle for your sanity.
If you are really contemplating long-distance travel and taking the horses then don't not consider a motor-home pulling your 2-horse trailer currently owned.
A very comfortable existence for you on the road long from home and your horses still going with you.
LQ-combo horse trailers sound wonderful but unless you refer to getting a really large trailer, it is not much room for the humans..
Keep in mind laws for driving these behemoth trailers around are changing for everyone ....or so is the discussion much closer to happening in reality.
Soon you will be required to have better and more expensive class of licenses when you get over certain sizes and weights...they cost money to get, money to keep and you must pass a practical road-driving test covering all aspects of being on the road and preparing to haul.
They also are talking about mandatory physical exams yearly for those driving...very similar to CDL license requirements.