Yes, Cold does effect the frequency but only by fractions of a second overnight(If you stay above the failure rating for the QC).I am unaware of the quality and age of the Q,C you have,but changing that would be next.However since you loose hours it very well could be anything from a cold solder to one of the QC leads all the way to a wire bond at the IC on the verge of disconection?
I do know that low quality Crystals (used in most digitals) shut down right arround the Temp you mention,So again you may want to start there while checking for good solder connections.
The Synchronar runs at extreemly low temperatures as a result of the gels protective/insulating qualities combined with a high Quality Crystal.
You can check out Digi-Key who supplies a wide selection of Quartz Crystals and someone else here may know the proper replacment.