It's possible to get frostbite when using an ice pack, if you don't do it properly. Ask any coach or PE teacher how to treat a twisted ankle and he or she is likely to say RICE -- rest, ice, compression and elevation. It's a tried and true method that works pretty well, as long as you follow a very important rule for icing the injury.
Don't put ice directly on the skin.
Water freezes at 32 degrees, but the ice that comes out of the freezer is likely to be much colder than that. Putting ice or any kind of chemical cold pack -- homemade or otherwise -- directly on skin can lead to frostbite rather quickly.
Even folks you'd think are familiar with the dangers of putting ice directly on the skin have managed to create frostbite from ice packs. One published case of a PE coach needing surgery to fix frostbite damage after using a bag of frozen fried potatoes illustrates how something that seems so minor can be devastating.
Another case of frostbite at a gym occurred after a staff member incorrectly instructed an injured client to place an ice pack directly on the skin when elevating her leg. The gym member got a palm-sized blister from the ice pack. It took 10 days of frostbite treatment, which was identical to burn treatment in this case, to heal her frostbite.
Frostbite from ice packs can be avoided. Don't put ice or ice packs directly on the skin. Put a towel or two -- or some other material of about the same thickness -- between the ice pack and the skin.
Never leave an ice pack on the injury for more than 20 minutes. The object of an ice pack is to cool the muscle without damaging the skin.
Graham, Colin A & James Stevenson. "Frozen chips: an unusual cause of severe frostbite injury." Br J Sports Med. 2000
Mac Auley, D.C. "Ice therapy: how good is the evidence?." Int J Sports Med. Jul 2001
O'Toole, G. & S. Rayatt. "Frostbite at the gym: a case report of an ice pack burn." Br J Sports Med. 1999