So far I have never had one that was tame enough to put a hat on. When I was living in a small apartment in the shop while building the house, there was a sliding window. Use to put some hay just outside it and then open it and talk to the deer and give them stuff. One fawn of a set of twins would come take crackers from my hand. His mom would stomp her hooves, but he liked those grahams to much. I called him Piglet. Twin was not so friendly. The deer that shelter in the hedge regularly are so used to me they let me get within a few feet. But, they are still nervous of me.
I just stand around, or move slowly and speak in a low calm tone. The bucks seem to be less afraid than the does. Bucky is one of the least nervous of the ones I have know. He will come right up on his own, but right now he makes me nervous because of the rut and bucks can get crazy then.
There used to be some fencing out behind the shop and once I noticed a doe acting odd. Then I see a tail of an upside down deer with its caught in the fence. Some times deer and elk don't clear the top wire of a fence and there front leg hangs up and turns the top two wires trapping their leg. I went out with a pair of wire cutters thinking this could get interesting. The trapped deer was a young fawn with a few spots left. It had been raining and it was cold and exhausted. I cut it loose with mom looking on from a few ft away. Its leg was skinned up pretty good, but not broken. Little guy just laid there. I carried it to the shop and mom followed me. There I took an old towel from inside the door and dried him off and that and the rubbing got him going again. He wanted loose so I let him go and he hobbled over to mom and she gave him a few licks and he went to suckling. Had a bit of a limp all summer and I called him Gimp. Don't know what happened to him much after that. They come and they go, usually one or 2 does and their kids stay close and a few others wonder in and out.
Another odd thing I noticed is the does baby sit. After the fawns get a bit of size, you will see the same doe and one day she will have one fawn with her, another day 2 or even 3, then none. Usually in the afternoon.