I'm up in Sweden right now and I know what you mean, but having read a lot of the posts here in the forum, many people suggest that X5's are not good cold weather cars. That leads me to think that as with everything electronic, moisture will play a big part in malfunctions.

I'd suggest first having the computer read for fault codes, as that might point straight to the problem. Everything that you mention seems to suggest the same or similar to mine, being an electrical problem.

If they find no error codes, have them reset the computer, and that might just fix your problem.