I wouldn't skin, bone, or do anything to a whitetail other than field dress it in the field. Dirt, hair, and leaves have to be in play while quartering, boning, and skinning in the field. I suspect there are ways to alleviate cross contamination. I just can't picture them other than being very meticulous which takes more time than I want to spend in the field with a downed deer.
I prefer hanging my deer to remove the skin, bones, and meat. Dragging on flat ground is no big deal. Uphill can be work.
To the OP, rinse it. Hair/dirt/sand will affect the taste more than a water rinse. If bloody water is dripping out of your grinder, strain or blot the meat prior to grinding.