In Ontario 22 cal. centerfire is not legal for big game for good reasons. Many have been mentioned already and they simply leave to many injured animals if everything is not perfect. They also tend to deflect easily in thick cover. The .243 I would consider minimum as it offers bullets in the 100 g. range and far more energy downrange compared to the .22 bullets. I personally use a 25-06 and have never had even large deer travel more than a few steps.

Best Wishes