I don't know what deer think or if they even do. Last weekend I put up a stand on some public land. It always seems like I make so much noise every deer in the county will be gone. This time was no exception. Anyway, I got the stand hung, had a sip of water, called my son to make sure he had his stand up okay, hung up and heard a noise at my feet. I looked down and there was a big old doe right under my stand. My bow was hanging on a limb with the arrows neatly tucked into my bow quiver. She kept walking on through. I stood up and nocked an arrow, but by the time I had a clear shot, she was too far away.
I've also had them stand and stare at me as I walked to within a few feet of them in the dark while using a green cap light. The wind was in my face. I've also busted some while walking in when it was just light enough to see without a light but too dark to shoot.
Bottom line...it doesn't make much difference. If you can be quiet and not get winded, I don't think the light hurts a thing. If you are loud and stinky, you are gonna get busted, light or no light.