Some yacht and sailing clubs, marinas, etc., have mast-up storage lots with an unobstructed path to a boat ramp or launch hoist/crane. If you can keep the boat in such a place, then you can have the convenience of keeping your rig up. Houston Yacht Club is one example that has a large area where boats can be stored. I believe your boat is too big for the Seabrook Sailing Club, which is for dinghies (centerboard boats).
-- There are special boat covers made for use when the mast is up.
--If you are going to be away from the boat for a long period, you could put messenger lines on your halyards and run them down out of the brutal Texas sun.
-- Of course, if a named storm approaches the area, you'd want to de-rig to either move your boat inland or at least reduce windage and damage.
-- It might be a good idea to visit the boat often enough to discourage bugs or critters from taking up residence within.
--Otherwise, if you don't have access to a good mast-up lot, the results might, unfortunately, be a bit of a shock.
-- Maybe you could revive this old-ish thread in trailersailor:
Galveston Bay/Clear Lake marinas for trailer sailboats