Well, there is a bit of a feeling of sadness for taking the life of a beautiful animal. But it is outweighed by a feeling of pride and gratitude.
Pride in my prowess and skill in moving quietly and shooting accurately, in testing myself against a creature that has senses much keener than my own. Pride that I can secure meat for myself and my family. Gratitude that I have the ability and means to hunt, and land on which to do so. And gratitude that the deer was created for the purpose of providing sustenance for man.