Well, deserts exist already, and if the world ends, then they will be post apocalyptic deserts. Nuclear weapons are not going to cause jungles to sprout up overnight in any of these arid locations, be it the Mojave, the Gobi, or what have you. So by default, these deserts are guaranteed to be post apocalyptic and will be so the very second the world "ends." A nuclear winter might occur, but an eventually is slower on the draw than instantaneously.