I live in the Frozen White North (AKA Canada) and unfortunately fly in cold weather for more cold months than warm. Since our winter temps are generally "Oh my Gawd, are you SERIOUS?" kind of temperatures, I've had to adapt in many directions. First of all, your UAV; it really should be left out in the elements to cool down completely before flying. As a general rule, I start the outside acclimation around 0C (32F). Below -20C I will only fly in wide open, unobstructed areas. That's seems to be the point where anything you bump with your multi will result in damage to your acct. You do not want to be messing with swapping out broken components at that temperature; even replacing a broken prop is onerous.
Don't fly Graupners, or other high-end carbon props. They will shatter with even the slightest contact with something. Buy, balance & mount some inexpensive props for cold weather flying.
Seriously re-think FPV flying in extreme cold. If you're a goggle flyer, you'll need to watch out for condensation inside the goggles clouding your view and potentially causing damage. If you fly with a monitor, know that they (LCD monitors) don't like cold. You can damage them just taking them outside on a cold winter day. Also, trying to FPV with flat, winter light can be vertigo inducing; you can't tell where the ground stops and the sky begins. It's potentially dangerous.
Here is my routine for batteries...if I know I'm flying later in the day, I throw the batteries I'm going to fly on the charger to peak them up. They come off the charger, and go into a Pelican case with a couple packages of desiccant and an air activated pocket hand warmer. The box is closed & latched, and it's the last thing to go out the door with me.
I usually will take a smaller 3S battery, 22-2500mah along just for compass calibrations, which I do every time I fly in the winter. I probably don't need to do the compass dance each time: I do it anyway. It doesn't hurt, it takes a few seconds, and I can be confident that nothing is off because it's cold out. I leave the lightweight battery plugged in until I'm ready to go, just to warm the electronics a bit, including the GoPro (powered from a ZenMuse gimbal on an f550) Once I have my transmitter mitt on and ready ( I use it for personal comfort; I find they do keep my hands warmer; my mitt has pockets for hand warmers,which I use as well so I don't have to wear gloves while flying), I swap out the small 3S batt for a warm flight battery. They come out of the case and go into a thin neoprene sleeve that I fabricated from an old mouse pad. They get plugged in immediately
When I fly, I don't see any real, measurable decrease in flight times. The batteries are nice and warm when they come out of the Pelican, and stay warm through discharge during the flight.
Once a battery is done, it goes in my coat pocket to avoid the chance of re-mounting them.
If it's really cold and the wind is up a bit, I also fly using a small hunting blind. It's a 1 man collapsable blind mounted on the back of a folding lawn chair. The top of the blind opens pretty wide so there is nothing blocking the transmitter, and it cuts the wind really well. I also have a small heater that mounts on a 1 lb. gas bottle that keeps me warm enough to fly very comfortably
