I've been hiking, climbing, camping and ski touring in the winter mountains since the 80s. I've been on several winter trips where people have fallen into streams. None of them required a fire to manage. Knowledge of modern clothing systems and shelter sufficed.
I've also been on a few trips where we bet our lives on making wood fires as a safety plan. These are remote and long ski tour day trips in which carrying normal winter safety gear (stove, sleeping bags) weighs too much and inhibits the ability to make the miles necessary to complete the route. A tarp, small wood stove (to start a large fire or manage a small scout fire), fixed blade and folding saw weigh less than the other gear. In many ways, I consider these trips as dangerous or more dangerous than above treeline trips. Obviously, above tree line, fires are impossible and big knives are counterproductive due to their unnecessary weight.
None of this justifies carrying a fixed blade out in the open while hiking on maintained trails though, which is at the core of the OPs first post. IMO, carrying a fixed blade out in the open on maintained trails on public lands simply attracts suspicion and attention.
I hiked and camped extensively in the Ventana Wilderness in the Big Sur area in California for several years. It's mountain lion territory. I can see the justification of carrying a fixed blade in an easily accessible manner. That said, if I'm really taking mountain lion (or grizzly or moose) attack seriously a) I'm doing other things to minimize the threat and to respond long before a knife becomes involved and b) if things get close, I want a fire arm and pepper spray before I want a knife.
https://www.nps.gov/pore/planyourvisit/yoursafety_mountainlions.htm