Sidewinder, as already mentioned, you really have to be concious of the wind and your movement. If on the ground stalking, you also have to be careful about noise...unless if the leaves are wet, that would help negate that challenge. A deer is extremely quick, so a shot on an alert deer using primitive equipment is very risky. Most likely if the deer knows something is wrong, they'll either "jump the string" completely, or you may wound them. I strive to have the deer completely at ease when I make my shot, thinking that everything is fine with their surroundings.
If you hunt off the ground, you might use a blind as an option when not stalking. Try to incorporate something already in the woods like a fallen tree or ditch, and you just add some cover to it as needed. Make sure you're down wind of where you expect the deer to come from. I like to hunt places where the structure of the terrain funnels the deer into a small area. This could be a bottle neck in the woods, or a steep ditch that they're only crossing at a certain location. You might carry a small stool of some type with you to the blind and clean the leaves away where any movement with your feet that you might have to make could be accomplished quietly. If you're comfortable, you won't figit and move as much which may cause a deer to spot that movement.
Of course a lot of this can be applied to treestand hunting which is what I personally prefer. I'm sure Indian's used elevated perches to hunt from as well as stalking. I respect you're wanting to try hunting off the ground...it is a challenge along with the equipment we use. But if we weren't after the challenge, we'd all be using rifles I suspect. I do hunt from a stand, but I hunt from a stand throughout the entire deer season in Tn., Sept. through Jan. 1st, using a selfbow.