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We have ours on the poured cement roof over the garage, which is a walkout from my office. This roof is a "rooftop garden," with scuppers that route the rainwater off the surface. The builder put steel beams in to hold this weight. Its open to the elements. We dump the water and clean the tub when June arrives because its too damned hot in the Missouri Ozarks in summer to get in a 100 degree hot tub. By September, things begin to cool a bit and we refill from the garden hose, put in the chemicals and we're set for eight or nine months.
Wife's counsins have one like ours. Their tub is in a game room with tile floor, converted from a two car garage. With the doors rolled down, the room is heated and the tub is used year round. In warm months, the garage doors are up and custom screens are in place. Moisture has not been a problem for them. Keep in mind, you'll need to attach a garden hose to the tub drain, so a floor drain would be a good idea, otherwise, you'll have to carry the water out in buckets.
Good luck.