This post is very very late ... but consider this getting you excited for the coming winter! There is this reservoir near me which people walk around - even in the winter. After a large snowstorm worn paths tend to form.
How far out of their way will people walk in order to stay on the "path"
No equations yet but it could depend on how steep an angle out of their way the path is heading or how sharply the path turns. It could also depend on the ratio of snow deepness off the path and on the path but this was not investigated.
One morning I managed to be the first person to walk the path after a large snowfall. I walked marched in several differently winding paths with my snowshoes until they were pretty worn (see below).
I made sure that they had "out of the way" angles slowly increasing, with increasing curvatures as well (sharp and smooth turns).
It turns out that the most important measure is the horizontal distance out of the way people will walk. Note that this bend follows my path exactly but they quickly break from it.
It turns out that people care more about horizontal distance than anything else in this matter. Also surprising - only the well traveled areas had this effect - in the lightly walked parts of the path, my "experiment" had no effect at all. My guess is that the highly traveled parts were mostly people who needed to get through the snow, but the less traveled parts were walked by people who expected to walk through snow and were therefore more prepared to forge their own path.