Standing in -21 shooting the Aurora I have found using a fleece, with a hand warmer as recommended above works well enough, but I don't have them close to the body of the lens because some get bloody hot initially.
I tried a fleece scarf wrapped around the lens with hand warmers inside this worked well but was restrictive when maintaining critical sharp focus (Easy to move the focus ring inadvertently unless you want to tape it).
Another idea that worked was a small computer processor fan on a rig blowing air over the lens,.... To much faffing though.
Wont go into all the rest of the things I tried, but the Mk5 is a Fleece Balaclava!
This is brilliant I place what would be the neck over the lens, and the hood part that would be over your head, over the camera body.
On the neck I had some Velcro cable tie that I could close up the neck around the Lenshood (this was later modified with some Velcro sewn in).
The advantages were the head part that flicks over the camera body is roomy enough to get your hands up inside, (As is the neck for Lens adjustment) or just quickly flip up the hood to check the camera settings . Dropping it down to protect the camera body itself, this also improves battery life etc.
I also sewed some little pouches inside to take hand warmers.
This was done because on one shoot I was using my old faithful Nikon D300 and my D700 (at the time) . By the time I had finished both cameras where completely white, pretty much, with frost... The D700 expired with an error, this thankfully turned out to be a communication problem between the Lens and the Body and came back to life after a very gradual bringing the cameras back to room temperature very slowly. The tripods were also white, then I made the mistake of grabbing the Aluminium one without gloves, I had to use a cup of luke warm coffee to remove it! So if you don't have a Carbon tripod consider covering an Ali one.
The other thing I got hold of was a little insulated box for my batteries, I throw a hand warmer in too, batteries die quick in the cold.
I have tried various hand warmers but the chemical ones (single use) seem best, unless you have some method of recharging the reusable ones where you are. (you can get a great big box from Costco if you know a member at a reasonable price).
Good Luck
Steve