Will cold weather break my laptop?

Situation:
It’s -5 °C outside and I’m bringing my laptop to school in my bag. I spend a lot of time walking outside in the cold. Then I go into the school where it’s 25 °C and fire up the laptop immediately. Note, I’m not using the laptop while outside, it’s on “sleep”, so the “operating temperature” in the manual is irrelevant I think.

What are the odds that this breaks/wears my laptop eventually, or shortens the battery life? Has this happened to anyone? Any way to protect the laptop without using an additional insulating bag?

Laptop model: Fujitsu-Siemens Amilo Pi-3525

P.S. Some days it snows (high humidity) and some days it doesn’t.

Solution:

I live in Montana, and we recently had a couple of really cold weather snaps (-22 °F, -30 °C), and I walk around with my laptop in my bag all the time. It should be okay, but especially when it’s cold be sure not to bang it around until it warms up a bit, because the plastic components become much more rigid and fragile in cold temperatures.