Bathtub drain backs up when weather is very cold...?

The bathroom is above the garage. The garage is not heated. I am uming that the drain must be freezing, since it only happens when the weather is below freezing for more than a full day. If water is collecting in the drain it must either have negative pitch or there must be a trap installed and the water in the trap is freezing causing a blockage. Anyone else seen this problem??? Any easy fixes?? I would have to cut a hole in the drywall of the ceiling in the garage to access it, but should I just remove the trap?? What problems could that cause?