In my town in NY we still have a few unpaved roads, at a town hall meeting it was expressed that some would like to leave those as is as it is part of the charm of the town, the residents who lived on those roads were not charmed by that at all.
If mud seeps up when it rains… the problem isn’t lack of paving, it probably has more to do with lack of drainage and lack of gravel. When they build a subdivision near us, the first step in roadbuilding is to dig 2 feet down and fill the path with gravel. No actually, the step before that is sewers.
I would instead suggest the first step is to look at the worst stretches, and see whether a few strategically places ditches and culverts would reduce the amount and duration of mud. Then dump more gravel on those places.