The reason these recommendations are made in relation to ice is because patients who have burning neuropathic pain and try to relieve that pain with ice. They over-use the ice, cause tissue damage which can become very severe and in turn can cause tissue necrosis. This is clearly catastrophic for anyone but for someone with CRPS really is a disaster.

Ice used correctly in accordance with a normal RICE type icing protocol will not do that and will not cause damage. If you have cold limbs it may be unpleasant in which case there is clearly no point in doing it.