Freezing a humidor

Tuesday morning as I got out of the bunk in my truck, I noticed that a bottle of water had frozen over night. Will this have any ill effect on a humidor? I'm not worried about the sticks, but the wood of the humidor. Would I be better off storing a different way? I take 30 to 40 sticks with me in the truck for a week or two. The lows have only been in the low 20's so far but could go much lower.

I'd put the humidor in a cooler - even a styrofoam cooler - or just use a cooler-dor - or use a couple of the bigger hard plastic humidors.

Thanks for the info. I'll cooler first.