Thanks for the kind comments!
It is certainly OK to use your TRX in wet and cold conditions. Keep in mind that (i) UV rays degrade nylon over time and (ii) salt air will, slowly, corrode the cam buckles and carabiner. It's certainly OK to take your TRX to the beach, or out on a cold day, etc. I do that all the time. But it's not advisable to leave the system permanently mounted outdoors where it will be exposed constantly to salt air or direct sunlight. Cold should make no difference whatsoever. I know folks who've taken their system on cross-country ski trips, hooked out under a tree, and used the TRX right there in the snow.
Good luck.