I think the term "singletrack" generally implies bikes are what the speaker has in mind, but the trails are just thinner (one person wide) and are sometimes restricted to people only, sometimes allow horses as well as bikes, and sometimes allow even motorcycles. The problem when they get muddy is that people go around the puddles, widen the trail, and destroy vegetation around them. Someone will eventually come close off that part of the trail to allow the plants to grow back. Rail trails are about the equivalent of bridleways, it look like!

Your photos are gorgeous You definitely have some mud to deal with though. I wonder if my doctor would count that as "off-road"...maybe I should go there and ride my bike instead!