Why is my foot cold after injury? is this normal?

It is NOT normal.: A very rare, but potentially dangerous and disabling condition following an injury is called regional pain syndrome (or reflex sympathetic dystrophy) which is a disturbance of the autonomic nerves. If not diagnosed and treated promptly, can lead to a lifetime of pain. There are other causes of a cold foot, like if a blood vessel was injured, but please go back to your doctor and get it checked.