My 25-20 Winchester...
sadly I don't actually have one of those...

. . . . I mean my 2520 John Deere has been running fine including in cold weather colder than today. Today was around 20°F and it started with reasonable vigor but the engine runs approximately a second and then promptly shuts off. I'm not going to mess with it tonight but figured tomorrow morning I'd better see what I can do.
There's fuel (treated with SeaFoam) in the tank but there was ice in the bottom of the bowl that collects condensation, so I shut off the fuel valve above it, took it in the house, thawed it out, and cleaned it. Reinstalling it and opening the fuel valve didn't help much, and at first, as expected, the engine had to turn over a bunch to move fuel before it would try to start. Then it was the same. It would start reasonably easily then after about 1 second quickly stop.
I'm thinking maybe there's ice in the fuel line someplace else, or that one of the engine cutoff switches is stuck. The ones I know of are on the dashboard implement switch that activates the PTO, one on the gear shift (or at least between it and the transmission someplace) which activates if it's not in neutral, and one under the seat that activates if you're not sitting in the tractor. It was in neutral, the power take off switch was pushed into the "off" position, and I was sitting in the seat, although I realize that switches often vulnerable to malfunction.
So I figured tomorrow I would back the pickup truck next to the tractor put a huge tarp over the tractor and the rear of the pickup and idle the truck for about 15 minutes to warm up the air (and hopefully gas line) under the tractor with exhaust, then try to start it. If that fails then I will bypass the seat switch temporarily, make sure I tap on or wiggle or lubricate the implement switch and transmission shift, and try again.
I'm reasonably good at diagnosing humans but sometimes not so good when it comes to machines. Am I missing something else I should check or try?