Good question. As a novice hiker back in 2001 a good fire helped more mentally than anything else, it’s amazing wht it can do for the spirit if you’re alone at camp and you can hear things in the woods.
As far as staying warm goes, thats tricky. I would assume that most people who hike in cold weather are prepared for it. I’ve hiked and camped out in 10* weather and the last thing on my mind was fire, just getting into bed and eating were top priority to retain the warmth generated by hiking.
If it was bitterly cold and i had all the right gear (down everything) then i may start a fire to warm the heart if i was in a protected spot and out of the wind/snow etc.
I was recently working on building a hoophouse structure here in Maine and the wind took the daily temps to around -25. A good wood fire definately saved my feet and hands on those days.
Cheers
Cheers