Sometime this Summer I bought an outdoor rated CFL and replaced one of three incandescents with it. The outdoor lights are used so seldom that it doesn't matter that much, but I was curious about cold weather performance. The last few days have provided enough cold weather that one might think there was a Global Warming demonstration being held in the area.
The light does come one, even at -18 F, though it does so slowly. Instant-on it is not. It seems to do nothing for moment, then the base ends of the tube start glowing, flickering slowly for a bit, before the glow grows through the rest of the tube. Then it's on, but not at full brightness. That takes a few minutes.
The "locker light" motion (passive IR, I suspect, not actual motion sensing) lights with LEDs are work just fine even in this frigid weather. The dollar store alkaline cells don't seem affected by the cold, at least not at the current drawn by the LEDs. It's very nice to not have to fumble around in the dark in this cold to find a keyhole or pushbutton. Putting these lights into place a few months back was a very good idea.
A couple years ago I had some trouble with the battery for the garage door opener remote control and figured it was not just battery age (since I replaced it recently) but cold, so I went and spent a bit on a lithium battery since those were supposed to be long-lived and cold-tolerant. That went dead a couple months ago and it seemed like it had a rather short life for what I had payed for the thing. I replaced it with a dollar store special. It's not even an alkaline, but a carbon-zinc thing. The last few frigid nights (lows have been in the -20 F region the last few nights) it's worked just fine.