I don't live in could places as some of you guys and gals do but, in my opinion and way of thinking, keeping the CA bottle in a container of warm water when/while you are applying CA would certainly be an advantage as the CA temp would hold right to the application point and then, to maintain/keep the CA at warmer temp while turning in the lathe, you either use a heat gun/hair dryer to give it a "hit" for a few seconds in between costs or, make life a little easier to yourself and get one of the small heaters with a fan and put it about 1 meter or 2, from the barrel you are turning.
These are great to warm an area and endup warming up a full room if let on long enough, they are a little heavy on power tough, the 1.500W can be not a financially effective way to warm up a room but certainly very effective for the purpose of creating a warmer environment around the lathe...!
Accelerator is also a must, I use it even in my hot(ish) to hot temps, not only hardens the CA in between coats but harden the CA very quickly for a light sand in between group coats...!:wink::biggrin:
Good luck!
Cheers
George