NO. Colds are caused by a virus.

This is an old wives tale but it has some truth in the fact that if you are very cold your immune system may be compromised and then you will be more susceptible to catching a cold but only if you have been in contact with another person with the virus. Colds & flu are a virus that you have to catch so not wearing socks will not give you a virus but if you are always cold which in turn runs you down then yes you may be more likely to catch something.