The question of this research topic is: How far can a person walk in a day? The answer is always: it depends. Once again, this is the least helpful response for someone who just needs to know what’s a reasonable distance for a human being to travel. Now, this is a topic I researched some time ago, and is buried in my notes. Also, I’ve tacked in my own opinion on the matter by applying my various, albeit limited, hiking and hunting experiences.
Easy terrain – a road, or well worn trail, with gradual slopes or short stretches of steeper terrain. This would include game trails. A fit person over relatively easy terrain can travel about 30 miles in an 8-10 hour day. If well trained, and pushing it, a person could plausibly go 40-50 miles. Keep in mind that over the course of 10 hours, stops have to be made for food and bodily functions.
Moderately difficult terrain – This would include some steep terrain in open forest with limited trails. Imagine a forest with lots of big mature trees, few thickets, some windfall trees mostly knee-deep grasses, bracken and similar foliage. A few creek fords might be thrown in there. My experience is that you could probably cover about 20 miles, pushing 30 in a full day. The terrain isn’t really that difficult, and the slow-down comes largely from navigating around obstacles, and being a little more careful with footing.
Hard terrain – This is where you have lots of steep bits, dense thickets of willow and alder (or similar depending on your climate). I’d say something like 10 miles per day would be reasonable. Part of this comes with elevation, you tire much faster when you climb, so you have to stop and rest more often. You may still cover a lot of ground, but you won’t make much actual distance across the landscape.
Painful terrain – Knee-deep (or deeper) fresh snow on reasonably flat ground, I bet you could make 10 miles, but it would hurt, and you couldn’t keep up the pace for long. On hard-packed snow, you might be able to make it closer to 20 or even 30 miles. The thing about walking through snow, even with snowshoes, is that it’s like walking with thirty pound weights on each leg.
Don’t ever do this terrain – Deep snow up the side of a mountain – A very fit person is going to make 600feet in an hour without having a heart attack. There will be a lot of switch backs, and slipping around on uncertain footing. In this case, it really does depend on how steep the mountain is. Bottom line is that over the course of a day you could make it up and over two or three 600 or 800 foot ridges, and the actual distance covered is going to be on the order of 3-5 miles or a lot less.
I’m not going to promise these are the best estimates ever, but this is generally what I think is reasonable for a fantasy book adventurer beating his or her way across some exotic landscape.