Being from Florida I gut immediately for 2 reasons.
1. Main reason ,it is esier to carry out with the weight of the intrals gone. Where I hunt you can not een use a cart. I have to put an orange vest over the deer and carry that puppy out. I did last year. I fell down 20 some times but I made it.
2. I was just brought up that way.
Once in the WMA check station, most guys skin immediately ,1/4 the deer and put him in the cooler.

Chuck