I seriously doubt anyone would use precious hauled water to put out a campfire. Maybe they would not admit it, but I bet they would just let the coals burn down and make sure they are cold when they leave.

You are talking winter backpacking with freezing temperatures. Does it ever snow? You could wait until after a snow and then melt snow for water. And at least when it is cold, you sweat less. It may help to slow down the pace- keep the pace purposefully slower than you are able to do, to minimize overheating. I try to breath through my nose and keep my mouth shut and adjust my pace to allow this. You get a lot less thirsty that way. It may take another hour to get to your destination.

I think most people have an overblown fear of running out of water and actually carry too much. If you are only on an overnight trip, although not fun, you could go without water on the way down. When I climbed long rock alpine routes 1 liter for a 10-12 hour climb was common. There is thirst, and then there is dangerous dehydration. The former you simply focus on climbing; the latter you enter the survival mode. I have been in a few very tight situations; not pleasant but survivable. You can survive only minutes without air; 2-3 days without water; up to 30 days + without food. I regularly plan on no food on the last day. It makes that after-hike meal even more sweet!

When my pack gets too heavy, I usually find that it is because of too much of all that little stuff, a few ounces here, a few there, and almost always stuff not needed. I limit myself to one pound of "extras". On some trips I leave the camera, on others I leave out an extra down sweater and decide that I simply will jump into the sleeping bag earlier. Sometimes I switch to no-cook if it is just an overnight trip. Sometimes I leave out the wading shoes and simply get my hiking shoes wet. I have three packs suited for different weights. If I can get the weight down, I can switch to the lighter pack, saving even more ounces. Sometimes I leave out the rain gear if the trip is only 2-3 days and the weather report is solidly no rain.