Freeze/thaw stability of hCG is high, as is stability in the fridge. I don't know the data off-hand for water, but available data in serum, whole blood, and urine indicates freeze/thaw stability of a minimum of 10 cycles and stability in refrigerated storage at 4 degrees C of 4 weeks for urine specifically.
From this data it can be extrapolated that stability in water when frozen or in the fridge is quite high. I can't speak for the light sensitivity to degradation though.
Bacteria growth when frozen will be minimal, but still potentially possible. When refrigerated the potential warrants concern.