Thank you for your question regarding your girl who has hurt her front leg. This is a rather worrying situation and hopefully there isn't too much damage done! If the paw is cold, this could just be a sign of her temperature, however it could also be a sign she is in shock or that there is an injury causing a lack of blood flow to the lower leg.
There are a few potential injuries that could cause this limping ranging form sprains, strains and ligament damage, to more severe injuries ranging from small chip fractures in their carpus (wrist) to complete breaks of their radius and ulna (antebrachium or forearm).
For this reason, if she is not walking on the leg at all, or only placing it now and then, I really would get her to your local Vet clinic as soon as possible and they can assess whether there is adequate blood getting to the leg and rule out systemic shock. Here the Vet will undertake a close examination of the forelimb and may even wish to x-ray the leg (which would be the ideal) in order to rule in or rule out a break.
If a fracture of any sort is ruled out and the blood supply to the limb appears fine, your Vet may then wish to send your girl home with antiinflammatory medication for a week or so to help numb the pain and reduce inflammation in the leg. If this is a fracture, obviously your girl will need a bit more work either at your Vet's or at a referral Veterinary surgery.
Best of luck with your girl and please do get her to your Vet as soon as you can if seems sore or if the paw is still very cold. Please reply if you need more advice won't you.
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Dr M D Edwards