What is the minimum temperature for FR-4 PCBs?
FR4 PCB is glass-reinforced epoxy laminate. Several research studies have been published of the effect of low temperatures on such material.


A specific quote from the paper "Dynamic failure behavior of glass/epoxy composites under low temperature using Charpy impact test method" (Shokrieh et al):


  it is found that failure mechanism changes from matrix cracking at room temperature to delamination and fiber breakage at low temperatures.


This study applied a temperature of -30oC, not low enough for spontaneous crystalline brittleness.
Another study, "The Influence of High and Low Temperatures on the impact properties of glass-epoxy composites" (Putic et al) takes the temperature down to -50oC, and finds the appearance of brittle cracks in the material at such temperatures. 




These are two key assumptions regarding the device touched upon in the question:


The freezer temperature will not reach as low as those used in these studies
There is limited risk of vibration or impact upon the actual circuit board, hence brittle cracks are unlikely but not ruled out


If either of these assumptions is invalid, the material in question needs to be reconsidered. There do exist special-purpose industrial ceramics / alumina PCB substrates designed specifically for extremely low temperatures, typically used for device deployment in space or in cryogenic equipment. Those materials might be more suitable in this case.

The point to note in such environments is the possible fracture of packages, casings and solder junctions for the electronic components on the board, not just the PCB itself.

A commonly recommended procedure for deploying circuit boards in extreme temperature conditions, is to bring the device to the desired temperature in slow stages, thus avoiding any rapid shrinkage or thermal shock to board or parts.