It could happen because of poor circulation, disorders of the nervous system, decreased metabolism from hypothyroidism (a low thyroid condition), diabetes, arteriosclerosis, peripheral vascular disease, Raynaud's phenomenon, neuropathy, or exposure to cold and frostbite.
As people may get cold feet when they are nervous, expression to "get cold feet" means to lose your desire or nerve to do something, be too fearful to undertake or complete an action.