To date, my experience is that deer always run away from myself with dog.
However, I suppose if startled or worried about their young it is perfectly feasible.
Can't say the same for cattle - definitely avoid them with a dog especially if they are with calves.
I have been attacked by a cow, within a couple of feet of being hit.
In 2009, I came over a rise to be confronted with >100 stags. Myself, with dog, actually ran towards them to get a good photo and they all ran away from us. If they had run towards us, we would have been in real trouble.