I honestly would draw while the deer is on the move, this may accomplish a few things:

1. It's more difficult for the deer to pick up your movement when he's moving.
2. The deer may actually stop to "see what the movement was" and if you're already drawn then... thunk!

Also, I've learned that when I'm hunting deer on heavily hunted public land I have my bow as close to me as possible and not on a hanger in the tree.

If there is a place to put a ground blind, that may be a viable option as well. Good Luck!