While the semiconductor die may still be capable of operating at cryo temperatures, an amplifier designed for 'normal temperatures' may not be biased to be able to operate there and still give optimum performance. The noise match may alter negating any improvment from the lower temperature, and the reliability of the components may be compromised. Differential rates of expansion, or in this case contraction may cause the components to break appart. I'm not sure anout the long term reliablilty of soldered joints below -60C either.
I don't want to sound pessimistic and say it will not work or that you should not try, just to be aware that the amplifier may not survive, but then it might. Keep the moisture out as much as possible, expanding ice crystals can cause a lot of damage if in the 'wrong' place.
Peter