I wouldn't roach it. He actually has a mane for a reason, and I don't think you should take it all off. I do keep my mare's mane shorter during the show season, but, I still leave her some mane.
Also, you do know that even with no mane, your boy is still going to roll in the mud. So you're still going to have a muddy neck to look at, with or without a mane. Horses love mud- especially white ones. Just let him be a horse.
"The barn taught me passion... Not the passion of winning-but rather the passion that you feel when you have nothing left but your love of something. The passion that is there when exhaustion steals your strength and frustration takes your hope."