Can a MOSFET operate at very low temperature?
Well if you take one example, say a IRF740 power MOSFET.

Look at the datasheet it will give you a maximum operating temperature, and a storage temperature. The low end of the storage temperature is -65deg.

Of course this would be a starting point. As soon as you start operation and switch a load through the FET, current will flow and inevitably cause the junction temperature to rise. The more current that flows the greater temperature rise. Generally electronics likes 'cold' temperatures, as in just above zero, but in some applications very cold ( -100 to -50 ) or even colder are needed to reduce thermal noise. Take a low noise RF amp as an example. 

Anyway to answer your question, yes they can operate at very low temperatures. And can get better efficiency at low temperatures because your Rds-on will be lower at lower temperatures.