It was important to keep one's mane clean. It simply was. Especially in the hotter months, as sweat began to soak it during the day, washing it properly was fundamental. One would start to have scabs on their scalp if going too long without properly cleaning their mane, to say nothing of how tangled and messy it would grow, or of how not properly keeping it clean could negatively impact one's mood. Of course, the act of caring for and cleaning one's mane was demanding, involving often the unfortunate removal of many hairs which had broken or been separated, but that too was a necessary part of life. With proper care, the amount of lost hair would hopefully be driven down.
The same was equally true for one's tail, for the most part at least. The skin on the flesh and bone part of it was not as delicate as one's scalp, and a lack of care not generally as damaging to one's mental well-being, but still it was something a pony had to take care of. It tended to get dirty quicker, too, being far closer to the ground and occasionally dragging against it, at the least constantly exposed to disturbed dust. It was however fortunately far easier to clean, being in a more easily accessible spot that did not risk precluding one's vision when washed, though it was no less hard to dry.
Drying always could be a problematic part of mane care. While simply twirling one's mane around was effective at discharging portions of the water, it tended to leave unpleasant effects to the mane's general shape, wrongs that would need to be righted with comb and brush and force of will. Towels were slow, and not every pony had the patience or time to put up with them. Drying spells or heating of other kinds, however, could and often would damage the mane, resulting counterproductive to the entire reasoning behind the process until that point.
Of course, it was true that some ponies didn't care about the health of their mane as much as others. Some did not care at all. To them washing was a mere obligation to be dealt with quickly and efficiently. It was a way to rid the mane of dirt and filth, but not a way to care for it. Other ponies would find such behaviour unreasonable and such a mindset impossible to understand. Not all ponies were the same, after all. Most ponies in fact were not. Only a few were.
Regardless of the case, simply leaving a mane wet and drenched was also a possibility. If one didn't mind the wait and was not bothered by the droplets, leaving it to slowly dry like so could be a healthy and viable way to approach things. Of course, leaving one's mane completely wet and drenched would indeed also have consequences when one was put atop the pyre to be burnt alive, though it would not suffice to snuff the flames.