Deer despite what you envision are not going to be a very important food source for you after the SHTF, at least not until after the human population has crashed. Sure a deer provides lots of meat and other useful products, but they will not last in most places. Every former hunter and every non-hunter is going to be shooting every deer they see year round. Deer can't take this much hunting pressure. I expect deer to go locally extinct across the vast majority of their range.
Deer only have 1 or 2 fawns a year and they don't start breeding until they are 1.5 years old. Half of the fawns will be bucks. So a doe must be 2.5 years old before they have successfully replaced themselves and 3.5 years before they contribute to population expansion. These numbers just aren't conducive to high hunting pressure.
There will be exceptions. Out west where the human population is low and the mountains are treacherous or swampy flood prone areas will allow the species to survive and to eventually expand to all of their old ranges eventually. However, expansion is slow as deer don't typically move too far from where they were born. So unless you capture and raise deer in a pen you will likely not have them around for a very long time. Deer were pushed to the brink of extinction in the east more than a hundred years ago and in a SHTF scenario it is inevitable that the process will be repeated.
Here is information on how to prepare a deer properly.
Clean and butcher a deer.