Hi can anxiety give you a cold all over feeling?

Not surprising. The cardiovascular effects of anxiety can constrict the small vessels that supply the skin (warming) leaving it feeling cooler. Each person may be more or less aware of a particular physical sensation change but there are many. Over time anxiety can actually do harm to bodies. It's a big reason to see a therapist (with or without medication) to learn how to reduce stress and anxiety. You can do it.