If I were sure there were nothing in the bylaws I would probably go ahead. But be sure. I know of two rules I have had to abide by while contracting for other people, Sheds had to be below fence level or sheds had to be sided and painted to match home. Something silly like this might get...
I think the term winterize is used for pools and spas that are shut down for the winter. If you plan to use and operate the tub this does not apply. Just be sure to keep the water warm enough that it does not freeze. Water freezing in the plumbing pipes could cause real damage.
Less expensive than the rubber roofing would be a vinyl liner used in above ground pools. Check with pool companies in your area that might have odd sized or rufused liners they might sell cheap.