I have a 20d, I've used it pretty much every day for over 18 months down here and never had any issues, I doubt very much you will have problems with either of yours. I have 2 batteries, I always keep 1 inside my pocket so it's warm and change over if I need to. Once you have swopped batteries put the old one back in your warm pocket and it will recover well enough to use it again if you have too.
Condensation is a real issue, I keep my camera cold pretty much all the time so it's always ready to go.
The best tip for down here is gloves, you need good thin gloves for taking pictures but your fingers get cold very quickly especially if it's windy. When I'm climbing or taking pictures or working outside I have a big pair of mittens that hang around my neck on a chord, I wear thin gloves inside so I can take my hands out, use my camera then pop my hands back into the mittens when they get cold. December on the Peninsular is stunning, 24hr daylight as you go further South and the sun can be deceptively warm, there is little ozone and you get burnt very quickly! Use loads of suncream.
Hope that helps.