What kinds of abilities does a Home Owners' Association (HOA) in the United States have to limit the use of antennas placed on a roof to an owner of a home in the area?
The only power that an HOA holds is that which is specified in the contract signed by the homeowner. This may limit towers or visible antennas. Hams have found quite a few ways around this:
It is possible to run a large dipole inside your roof rather than outside, supporting it from the main roof beam. You could use an off-center fed or loaded dipole to get multi-band coverage.
It is possible to run a horizontal antenna concealed under the eaves of your house
It is possible to use a new or existing vertical metal object such as a flagpole as an antenna
It is possible to conceal many types of antenna in a tree or yard
It is possible and even ideal to conceal radial wires (used to improve the ground plane) underground
Some hams have had success challenging these HOA rules in court on the grounds that they interfere with emergency communications
I share the same pain, I bought into a Home with HOA BEFORE I got interested in HAM.
A good reference for ideas for HOA restricted Antennas can be found in the ARRL's book "Small Antennas for Small Spaces". It's chalk full of ideas. (ARRL: https://www.arrl.org/shop/Small-Antennas-for-Small-Spaces-2nd-Edition/)
Check YouTube, there are lots of creative ideas that appear to work. I myself have purchased a speaker stand and mounted a J-Pole on it and put it out at night or when I need to get on the air. Seems to work for me pretty well with my HT. Now to get my IC-7100 up and running. :)
I saw one where a Ham put an Antenna in a flower pot and decorated it with fake/plastic flower vines.
- A fellow like minded Ham