Proper EHU leads are generally made from "Arctic" flex (or something similar). Normal PVC cables shouldn't be "worked" (IE: moved about) in temperatures below freezing, whereas Arctic flex will remain pliable down to much lower temperatures.
This "Arctic" flex is also much harder wearing than normal flex, but for what you are describing, after the EHU unit, just to run power around the tent, your reel will be fine.
Don't forget, anything past that proper, protected EHU device is fully protected. Camp site electrics may even be considered too well protected in many respects, as they have so many RCDs or RCCBs in line, this is what results in them tripping so much. It's what is known in the trade as "nuisance tripping", a necessary evil of making sure everyone is properly protected.
Oh yes, & you're right; you should always try to unroll all of your lead so it can dissipate it's heat safely.










