Well, just came in from the great experiment, and back to the drawing board! I had the backpack and tube inside my windproof, but outside my fleece and the tube froze up in 10 minutes. I put everything under the fleec and an hour and a half later it was still frozen.

Conclusion: Don't let it freeze up in the first place, it takes a lot to thaw it out! Next time I'll try putting it under my fleece in the first place. BTW, even though the tube and mouthpiece didn't thaw, I was sweating!

... to be continued.

PS Just saw KevinG's post, I'll have to get me one of those!