Where we lived in Utah, before moving to Florida, if the fall weather was warm and dry, the deer would migrate down the mountainsides into people's gardens where there was still green forage to eat, because of course the gardens were irrigated. I'm sure it's the same in other mountain, desert or cold winter areas.
As the nights got colder and more plants died back, yes, they would feed on anything that was left with green on it. If you didn't scare the local herd away early on, they would even feed on the rose bush canes, and dormant evergreens, and then eat the bark off the trees which really did a lot of damage. So it's a good idea to establish a 'perimeter' for the plants you really care about, using scent deterrents and other means, and plant the deer resistant plants outside of that.
Oh, I was reminded that someone gave me a tip to hang old computer discs around the yard, for reflection and motion. My critters got used to them pretty quickly, but hey, it's a use for some old useless pieces of plastic anyway.