One or two thorough soakings should do it. Test with a moisture meter, and soak them again by dunking the pot when the meter indicates they are on the dry side.

DO NOT PRUNE: Wait until you give the plant a chance to bud out some new leaves. When you are 100% sure what is dead and what is not, prune off the dead stuff.

They grow well in AZ at 110+, with just a couple of soakings a month.

Bougainvilleas are capable of dormancy so I'd think it would resort to going dormant rather than just dying.

In tropical plants that cannot survive freezing, the whole purpose of dormancy is to survive drought rather than cold.

No experience with bougainvillea, but my hunch is that the leaf-drop and dead-looking appearance is just exactly what the plants are adapted to do in these conditions. Don't be heartbroken if all the stunted leaves fall off; the plants may just do that in the process of regenerating new ones.