I unfortunately do the bodywork on my families cars, and I live in Maine. I do all my resin/jelly/rondo work (yup rondo on cars) outside year round. All you need is a heatgun and mix the resin a little hot (extra hardener). The Resin/rondo mix will be soft until fully cured and just make sure you don't apply to much heat or it will bubble (you'll do it once before you get the hang of it). Once it cools down heat it one more time and that's usually enough to cure it of it's above 20 degrees F. Below 20 I just babysit it, and attempt to keep my fingers thawed . So it can be done in cold weather but it's a bit painful (no pain no gai.... erm inspection ).
Also like said earlier keep the resin/harder warm when mixing, I keep them in the house then mix them as soon as I go outside with little issue, but you'll need to be quick. If it's really cold then the mix might flow a little thick since it will inevitably cool down while applying it.
On the hotbox issue since your keeping large amounts of highly flammable fumes in a enclosed area you'll need to make sure everything is explosion proof like in a paint booth and be careful when opening the door.