A thermal jacket makes things worse - guaranteed.
As the butane evaporates, it cools the liquid left behind. Normally conduction from the air outside through the metal bottle helps stop this temperature drop from getting too large so the usual "stops working at zero centigrade is fairly close. If you insulate the bottle the zero degrees point will be reached at a higher outside temperature than without.
Of course if the air temperature is way below freezing, nothing is going to make a lot of difference unless you can provide external heat to the b ottle. In my Hobby, good German design meant that the pump suction line was run hard up against the uninsulated wheel arch so while we were camped in Germany for the first night, the pipe froze. I had to dismantle the cupboard to get at it to relocate the pipe and insulate the wheel arch. While I was about it I ran a 1" extension from the heating system to blow hot air under all the cupboards to make doubly sure nothing would freeze. A fortuitous result is the hot air blows underneath the floor of the gas locker and keeps it just warm enough that using butane is problem free.
Last camping spot a brit in a large MH was using a butane bottle sat outside on the ground. Heater went off at 2am when the outside temp was close to zero and they froze. Next day he got out some old quilts and foil and insulated the bottle and hose. I explained to him that it would only make things worse - but hey, what would an Australian know about cold weather camping (a hell of a lot actually - all learned from forums such as this one and other US ones). Next night was 2 degrees warmer but he still ended up freezing. We were snug as bugs in a rug both nights.
