Tape isn't designed for high pressure applications but considering the cost of a new air mattress, it may be worth a try however the process would be to cover the leak with a small patch of tape, slightly bigger than the hole or tear in the air mattress or inflatable. Apply the patch using firm pressure removing all air bubbles.

Despite the fact that most inflatable hot tubs are not rated for use in air temperatures below 40° F, it is common for people to use their portable hot tubs in the winter time.

Not as good as more expensive models but not to shabby either and one that can certainly be managed. While an inflatable hot tub might offer reasonable thermal protection there is one other aspect common to most that will affect water temperature. The air used to power the bubble jets comes from outside.