I would never cut it that's for sure. And is it really that big a deal?? A horse is a horse and they are going to get dirty. Also the more oily stuff you add, yes the more dirt it will collect. I have a Perlino filly and I just leave hers alone. When I do go and brush it I use the mane and tail detangler spray and that stuff always gets out the dirt and keeps it from tangling too bad. If you for some reason HAVE to have it near perfect all the time, then yes do a sleazy but I just don't feel it is fair to the horse to have that on all the time.
I have my hair messy at all times except for going out, and I am the same way with my horses. If they ain't going out riding anywhere, I just leave their hair alone unless I am grooming then I just only brush it.