Symptom Development. Cold symptoms usually develop within 2 to 3 days of exposure to the virus. However, a person may not know when he has been exposed to a cold virus because individuals may remain contagious after their symptoms disappear.Also, viruses that cause colds may exist on eating utensils and other surfaces.ymptom Development. Cold symptoms usually develop within 2 to 3 days of exposure to the virus. However, a person may not know when he has been exposed to a cold virus because individuals may remain contagious after their symptoms disappear.