I hear neuropathy can cause parts of the body to feel cold. but would they also feel cold to the touch? and could touching cold things bring it on?

Neuropathy typically causes altered sensation including temperature change. However, the extremity would not feel cold to the touch to someone else. A cold extremity usually implies a shunting away of blood flow to the extremity (vascular issue). Touching cold items would not bring on neuropathy but frostbite could through direct nerve damage. Have a physician assess you for clarity about this