Wow, that really does, doesn't it? I did the same thing, but not because of a deer. A car was disabled in the left lane on a rainy, wet 3-lane highway bridge. I tapped my brakes to slow down and went flying/spinning to the right, narrowly missing the side of the bridge, then across 3 lanes to the other side, and ended up facing oncoming traffic, right behind the disabled vehicle! I was positioned as if I was gonna jump-start him! Yeah, a lucky day since I didn't hit anything, and no one hit me! (Yes, Guardian Angels exist! )
There's no feeling more helpless than spinning like that. You're in the hands of fate.