The key, key factor, other than shot placement, is bullet construction. The reason that .223 is ordinarily such a bad choice for deer hunting is not because it's too weak - it's marginal perhaps, but not too weak - the reason is because uneducated people will use milsurp ball ammo in 55 or 62 gr bullets, or light varminter bullets, instead of good hunting bullets - the ball or fragmenting ammo is the culprit which causes poor performance and wounding. You'll get strong opinions on both sides, but I have changed my tune in the last few years and think that .223 is enough for our smaller southern deer, *IF*, and ONLY IF you are using expanding soft point (or ballistic tip) hunting bullets. Even with vitals shots. Still, if/when I hunt deer with my .223, as I plan to, I'm going to use neck shots only just in case, and use Win Powerpoint 64 grain ammo, or handloads. Oddly enough, I'd rather have a .223 than a .22-250 *IF* making a vitals shot on a deer, because it can penetrate better (being both slower and having a better choice of heavy bullets due to common twist rates of 1 in 9 and such). But *IF* on the other hand, I was going for neck shots only, I'd prefer a .22-250 with a light fast bullet, over a .223. Still, if all I have is a .223, and no .22-250, then all things being equal, I'd rather take the neck shot over the vitals shot, in case it's quartering toward - don't want to have to go through bone. All depends on the specifics.
So bottom line, go for it - but please please use good quality bullets/ammo - NOT military ball (spire point) or varminter ammo. Use a 62-75 grain hunting bullet. As I say, the Winchester PowerPoint 64 is a decent deer load. If you do shoot at a deer's vital zone, wait for the broadside or preferably, the *slightly* quartering away shot - not quartering toward, and not heavily quartering away (more than about 30 degree angle) . If the deer is broadside, take the shot when the near leg moves forward, to move the bone out of the way, in case you shoot too far forward accidentally.
Now, if I ever make it to Alberta, CAN, or anywhere up that far, I'm going to use a .243 bare minimum, and probably a .270. Them deer get up to 300 lbs!! The biggest deer I've shot around here was only 123 lbs field-dressed (in Eastern OK), and most does are only 85-90 lbs mature. Now they do get quite a bit bigger in Western OK, however....