Just like people and cattle, deer are killed by tornadoes. Most tornado related deaths are caused by impact with heavy objects (either the person/animal hitting an object as they are being thrown by the tornado, or an object airborn stricking the person/animal). Also, being impaled by small flying objects can be quite lethal. And it doesn't have to be a "hard' object. I've seen numerous instances of grass blades impaling trees and walls, and recently even a thin piece of cardboard cutting half-way through a brick wall.

Animals certainly have the ability to notice and react to the approach of large storm systems, especially hurricanes ("feel" the drop in atmospheric pressure) but their reactions are usually just increased feeding activity in anticipation of possible long-term disruptions in food availability. The pressure drop associated with a tornado is so localized that by the time an animal/person felt it, it is too late. Considering in most Southeastern tornado outbreaks the forward speed of the tornado is so great (often 40-70 MPH) that an animal would not be able to get out of the way before the tornado overtakes them. In addition, would they have the cognitive ability to understand how to get out of the way of a tornado? Considering most people don't, I doubt an animal would.

Tornado damage can be the best natural habitat available for deer. I've seen several properties that were greatly improved for deer production by tornado damage. In future years, lots of food and cover production.