When I think about weather in ApW, I keep flashing to 'I Am Legend', which is a mediocre movie, but a great alternate depiction of an apocalypse - all overgrown, with trees poking out through roofs, and windows covered with ivy, and hedges that were once polite little borders now grown to weird tangled walls of thorns. I like the idea of playing 'normal' off 'apocalyptica' - maybe the weather's just dandy most days, but every couple weeks there's a day when the sky goes orange from pollution, or the wind brings such enticing scents that people do stupid shit, or the fog is so thick with maelstrom that going out in it is rolling weird+2 right there.
Our current game is set in Las Vegas, so yeah, hot, dry, desert-ish, nasty.
The game I'm planning, there's lots of trees and green, but sometimes acid rain so strong it bleaches what it hits, so everything's dotted with pale spots. Wind, frequent, and not sweet when it blows from the Cut. Sometimes you get days of glorious sun, sometimes you get snow so deep it kills, and sometimes the acid in the snow burns your hands.