You should have yourself checked for exercise induced asthma. A normal healthy person should be able to breathe even at -50C. What you really need to worry about is frostbite. I recommend a neoprene face mask that has holes in it to allow you to breathe. I have something like this from Amazon. I'd also recommend windproof underwear (if you're a dude) and windproof jacket and pants. I've been running outside all year round from +40C to -40C .
I wear a face mask similar to this when the temps drop. What I have found is the need for the holes for the nose & mouth for my breath to escape. This aids in preventing my glasses fogging up. I also wear a separate beanie style hat, goggles & a neck gaiter. I realize they sell this setup (excluding goggles) as 1 piece but I find by having separate pieces I can use them individually as needed based on my comfort needs.
Hope that helps!
Just touching on the face pro, I'd largely recommend a solid face pro over just cloth. Metal mesh or Polymer or something are almost always superior. It also varies on what the fields require, some are strict about having hardened full face protection. In my experience, just layered cloth can still give you a chipped tooth if your mouth was open and you were shot from close range. At the very least if you insist on cloth face pro, the Neoprene masks like This are fairly protective. Personally I've taken to one of these because it uses stronger mesh over the important bits and the soft sides doesn't really interfere with aiming.