The Lyman reloading manual specifically states that you should not use 223 on deer, and it is not allowed in many states and provinces. Usually the caliber restriction is set to .243+.
The thing that a lot of people, and fudds, don't seem to realize is that modern bullets make more difference than anything. People still quote Elmer Keith and Cooper as though they have relevance in today's hunting world. Here's a tip for you, they don't; With Barnes TSX bullets, Winchester XP3's, and modern smokeless powders, everything changed. The old argument that big fat bullets are best was 'maybe' correct back in the 1950's when you hunted with boolits. We now use medium bore cartridges that go about 2700+ fps in rifles that can make groups at 500 yards, unlike most lever guns.
It's not so much about the caliber anymore as it is the bullet construction. You can get TSX bullets in 223, and I wouldn't hesitate at to use them on deer if it's all I had, but it wouldn't be my first choice. I'd stick with something in 30cal, be it a 30-30, .308, or 300win mag for deer.