Here are some assumptions I've made that make me think being cold does increase the chance of illness:
• Feeling cold increases stress. ⇒ Stress weakens the immune system.
• Being cold expends energy. ⇒ Fighting a virus requires energy.
• Being cold increases blood pressure. ⇒ High blood pressure is not conductive to good health.
• The cold reduces circulation. ⇒ Reduced circulation is detrimental to health.