This subject of using .223 calibers for deer tends to stir up a lot of emotion.
As the posts demonstrate, you certainly can kill deer with a .22-250, assuming of course that it's a legal caliber in your area.
The question that only you can answer is should you?
This depends on a combination of your hunting area/conditions, your skill, and your own personal ethics. The main ethical point at stake is your belief about the .22-250's ability to deliver a quick and clean kill while minimizing the chance that an animal may be wounded and either suffer needlessly or escape only to die later.
While it obviously works for some people, it doesn't work for me. We hunt in areas where the chance for bullet deflection due to brush and tall grass is just too high. The cover also makes tracking wounded animals very difficult and time consuming. Finally, I simply believe strongly that we have an ethical obligation to use a tool that is most likely to result in a quick kill and I have several other guns in the gun cabinet that are far more capable in this regard.
But YMMV.
Grouse