If all you see is hair, with a 5x scope, the deer is close enough for you to just point shoot (or "no scope" for the CoD fans among us).
I like .303 Brit with a 174 or 180 grain bullet and 6.5x55 Swede with a 140 grain bullet.
I really like Hawk Bullets.
Dead soft lead core/dead soft, pure copper jacket=perfect mushroom/deep penetration DRT deer.
When I bought my first 5.56 poodle-shooter, I thought it would be cool to take a deer with it and rub it in the faces of all the old farts who insisted upon using cartridges appropriate for deer.
I was going to show them.
And it worked great as long as I got a perfect cervical spine or brain stem shot.
For pump house shots, it failed miserably far more often than not.
It will do the job with perfect placement.
Trouble is, animals seem to revel in giving us far less than perfect broadside shots.
I don't take chances on losing meat or causing an animal to suffer.
Don't get me wrong, aside from eating the meat, the kill is my favorite part of the hunt. It's a huge primal adrenaline rush.
But I don't want any animal to suffer. Except spiders.
With so many cartridges that are exponentially better than .223 for big game, there is no reason to use it on deer/hogs.
If recoil sensitivity is a problem, you don't have to use .30-06, .444, or .45-70.
6.5x55, .260 Remington, 7mm-08, .257 Roberts, and .303 Brit are fantastic deer rounds that aren't hard kickers.
.30-30 has killed a helluva lot of deer.
.35 Remington is even better.
.243 with 100 grain bullets is very good for smaller-than-Northern whitetail.
Heck, a great deer rifle can be had for a lot less than an AR.
As someone else has mentioned, a .308 AR is a great choice, if you want an AR style deer rifle.