When you get cold,there will be much bacteria in your hands and during the process of putting contacts in and getting them out, the contacts can easily get contaminated. So you'd better not wear contacts when getting a cold.
Yes. When you get cold, your eyes will get infected and some germs are easy to develop in your eyes. If you wear contacts, the germs will spread to your contacts. Then your eyes may feel really uncomfortable or get irritated while wearing them.