I would say with near absolute confidence you were witnessing that buck dreaming. I'm a neuroscientist by trade, admittedly don't specialize in sleep, yet it's an interesting topic that I can add a few facts/opinions to the topic.
One neat factoid is that all vertebrate organisms sleep. Even marine mammals like whales that need to breath at the surface sleep by "shutting down" as it were one side of the brain at a time.
Now dreams are something all together different from just sleeping in within itself. Now getting more into just my opinion, till I do some more homework, but I believe dreaming associates with the cerebral cortex (the wrinkled part that is visible from any brain picture we typically see in pictures). A region well developed in all mammals. Other vertebrates like reptiles have some cortex, yet not to the extend mammals do.
But trying not to stray to to far from the original point, deer definitely have a well developed cerebral cortex, and therefore I imagine can have some pretty vivid dreams of delicate does. The unique part is just catching a buck exhausted enough to enter a deep enough sleep to actually be dreaming...instead of just dozing or on partial alert. But, when ladies are on the mind...caution typically does get tossed to the wind.
Sorry all about getting a bit technical, this is just something I find fascinating!