Not an expert. Just a random guy thinking out loud.

To burn you have to dry out the fuel matter and warm it up to its combustion T.

If the air is -50, the fire has to give up enough enthalpy to not just dry up and warm up the wood, but also melt the water in the fuel. That energy cost is huge.

That cold air is dense won’t come close to overcoming the enthalpy of melting and having to dry the fuel.

Also that the air is “dry” is irrelevant at -50C. The air is dry because it can’t hold onto moisture so it won’t dry out the fuel. Also, the water in the fuel is frozen so even if the air was relatively dry there would still be a huge kinetic barrier to sublimation.

I’m not an expert either but I have experience with getting fires to burn. Starting a fire in the cold is quite a bit harder. Mostly because if it’s cold, then it’s the middle of winter, and that means the kindling is covered with ice and snow, which has to be melted and evaporated off. A dry log has a lot of potential energy in it. A frozen log full of water and snow has zero or even negative potential energy, as in, even if you get it to burn it might take more heat out of the fire because of the ice than it adds back by burning.

But, that might not apply to peat fires because 1) larger, hotter fires make more efficient use of fuel, especially if they are in some insulated space where all the heat is not going straight into the atmosphere and 2) the peat might be dry.

Scouts learn to start a fire in any weather - even cold rain. You split the log and use the dry wood inside for kindling. Wood takes a season to dry in the first place, and isn't going to get wet (inside) just because it's raining. FWIW

And peat is nowhere near as dense or insulating as wood. Wood doesn’t really want to change temperatures easily, which is partially why we make floors out of it.

But it’s also cold. A fire stops burning when it cools below a certain temperate, cold air means a fire has to produce a lot more energy to continue.

Any fire with flames is something around 600C and up to even double that. Air is relatively cheap to heat up. I'd wager the combustion process, once fully started, won't suffer much if the ambient temperature is -30C or +30C: the fire is still on a temperature scale that's an order of magnitude higher.

Even on a summer day a good breeze of wind or just blowing into the fire too hard yourself will put it out but only if it was just starting. Once the fire is rooted in something more solid, combustible material it will easily heat up any fresh air that is conveyed into the fire.

Air is cheap to warm.

Water in fuel is expensive

Though if this is a peat fire the water in the peat may have partially evacuated during the freezing process - I'm not so certain that the volume needing to be sent from ice -> water -> vapor would take more energy than the larger volume sent from water -> vapor... I really have no knowledge of ratios here but there are at least some processes working against increasing the amount of energy that needs to be expended to heat the surrounds.

Additionally, if this fire is mostly underground then it's likely that you've got some oven action going on where a lot of the heat produced by the fire isn't just whisked away by air to dissipate to nothingness - instead it's trapped by the insulation of earth and being converted into phase changes more efficiently.

> a lot more energy

Not relatively. The difference is still a small fraction of the total energy needed even on the hottest day.

Denser air also means that fire needs to push out more nitrogen in order to spread.