When I was little (oh yeah... that was a few years ago), My family had a huge... 12' tall bougainvillea in the front yard. My neighbor has a gorgeous bougainvillea that stands right in my line of sight from my kitchen window. Both of those evergreen bushes never seemed to freeze back.
However, I can't seem to keep this tropical plant from looking dead and shriveled up every winter. They do regrow some in the spring, but they often look like straggled sticks with a few leaves and glowing red booms here and there.
Every year, the low Arizona deserts have a hard freeze. The tropical plants are very frost tender and will always have some foliage damage.
The good news is... they always seem to bounce back in the spring.
You can protect a frost tender plant by covering it with a frost cloth, old sheets or a piece of burlap. The cover must drape all the way to the ground. This will trap the rising heat from the ground surface.
Five Frost Tolerant Perennials For The Low Desert
Rain Lily - Pink - Apricot flowers with dense tufts of a grassy like foliage.
Native Fleabane - Daisy type white flowers with a tint of pink or lavender.
Globe Mallow - Bright Red flowers with a cup shape. The branches on this bush are about 2' long and the bush can grow up to 3 ' wide.
Hill Country Penstemon - Perenial with spikes of pink - red flowers. Grows up to 2' wide.
Desert Marigold - Bright Yellow Daisy style flower with long stems on a gray - green bush. Will grow to about 1 foot tall and wide.