When I was in Georgia hunting, the (much ) smaller deer made it very easy to quickly get back to camp to hoist on a gambrel and gut very neatly.
In NY most deer you want to gut first...it also as already mentioned, getst them cooling sooner. It realy isn't a good idea to open up the cavity in the field more than just from stern to the edge of the rib cage at that time to minimize getting soil, leaves,etc. inside....think quality of meat. the only trickly part in my opinion is avoiding puncturing the bladder if urine is in it. that takes some finesse...if it does squirt some pee, no crisis, just rinse it off as quick as you can.Am I remembering that Alberta is your local? if so, your critters are plenty big, and you aren't going to want to hoist them with a gambrel in the field on your own anyway.