My take is that they get hotter and don't last as long in an oxygen rich environment. I suppose they could burn but in freezing cold weather, I don't see it. They definitely have more airflow on the top, with vents, than on the bottom.
I climbed a few 20k+ peaks in Peru. Early in the trip, at a col just below the final obstacle, a 1000' "easy" ice climb. I figured with hanging belays I'd be colder, so put foot warmers in my boots. They never got going and took up space in the boots. I ended up with some minor nip because of this. On the decent, while slogging down the glacier the next day, I noticed them come to life. By this point they were in my pocket. I think it was approximately 16k' or so, and they started working. More than 24 hours after I removed the package.
Lesson learned. A quality pair of socks and some room to wiggle my toes kept me warmer.
My toes occasionally go numb in any weather on the bike. Depending on the shoes. I could see freezing a foot and not realizing it until too late. I put dog doo bags over my socks, the put on shoes. Keeps the wind off.