You said a mouthful there Ski. We definitely over-estimate the cognitive ability of deer. Although it's impossible to know for sure, we assume that to have ANY ability to reason, the animal must have an imagination. In essence, the animal must be able to go through the "what ifs" of cause and effect to reason. As far as we can tell, no animal besides ourselves has an imagination, hence no animal but ourselves can reason ("If I do this, this might happen. If I do that, that might happen").
Now as for their physical senses, I think we seriously underestimate some of their physical senses, especially their sense of smell. We underestimate it because we humans cannot conceptualize having such a finely tuned sense. On the flip side, we overestimate their hearing. Brain function studies suggest a deer's sense of hearing is only slightly better than ours. They just react to what they do hear more quickly than we do.
Another mental ability we underestimate is a deer's sense of spatial awareness. And by that, I mean they will react very differently to the same stimuli based on where they are. Exposure to a particular human's scent in an area where they encounter it all the time, but it has never caused them harm there, will elicit no response. Contact with that same person's scent in an area where human scent only occurs during hunting season, and that scent may cause a very sudden flight response.