I'm with Heart Shot....cleaned both my deer this past weekend that way--we have a skinning rack at our lease. Head down....Front legs and head off like Deadeye first to get them out of the way, then cut from hock to hock and skin like sock. Zip tie on the anal tube when I get to the tail. Cut the anal tube on the outside of the zip tie when I cut the tail off, then final step, when dropping guts down is to pull the tube with zip tie through the pelvis to keep that area clean.
Minimal hair but only at the top on those initial cuts. I carry about 15 gallons of water with me every time I hunt to wash down as I go. I blew out a shoulder Saturday, so I put that to the side and cut out all shredded meat and bone and wash really good before putting in cooler. No bloody meat goes in cooler. Anything with a speck of hair or blood is rinsed off first.
I work my way from the neck UP to the hams. Cut neck meat, then backstraps, then anything I can get around the ribs or the belly. Cut the neck off...lower the hoist. Work the ribcage waist area....some real tender meat along the belly. When I am getting those tender cuts, the guts are actually open and exposed but usually stay right in the rib cage like a cup. Once I get the belly as good as I dare, I cut the spine (with hacksaw) that drops the ribs with guts into the bucket.
Then I take the inner loins and cut the spine just below the hams. Then I hacksaw the hams to split in half. Put them on the table and cut off the rear legs and wash really good as this is the one place I might have a couple of pieces of hair.
All meat is layered with ice (I bring ice every hunt) and drained daily until goes to the processor.
Sorry that was way too long....