Icing doesn't happen below about -40 C because moisture in the air at those temperatures becomes ice crystals which don't freeze to aircraft. At least not to aluminum normal aircraft. No idea whether it's the same for a solar drone.

Yes, the stratosphere has some tough environmental challenges like these low temperatures. To retain enough battery capacity, heating elements are required. The same is true for other onboard electronics.

Interestingly, because the stratosphere’s air is so thin, heat generated by the aircraft isn’t lost as fast to the surrounding air as at sea-level.

As mentioned by th0mas88, humidity is pretty low and icing typically doesn’t occur at these altitudes.