Is it safe to store electronics in a storage unit that is not heated?

There should be no problem storing your electronics in a storage unit. The only concern would be moisture. If it is one of those garage door type units then moisture can get inside and damage the components when powered up again. If you have no choice.

Try making them water proof as possible and when you remove them for use, leave them at room temperature for a few days. This should evaporate any of the trapped moisture.