If you are on an antibiotic can you catch a cold from being wet and cold?

No, if you catch a cold it is because you have been exposed to a common cold virus...being wet and cold is not a factor of catching a cold. You may become ill from exposure to the elements (hypothermia, frostbite, etc.) but you can not catch a cold without being infected by a cold virus.

Being on an antibiotic would make no difference since it would be for treating a bacterial infection. The common cold is caused by viruses and are not affected by antibiotics. Antibiotics do not prevent viral infections, but are sometimes used that way in a prophylactic measure against bacteria. However, going in public (wet or dry and cold or hot) with with a fever (indicating you are still fighting an active bacterial infection) is not a good idea for infection control.

You often hear it said that being cold can "weaken" your immune system, but that is not correct unless you are talking about the medical condition of hypothermia. Hypothermia is believed to weaken the immune systems of some people. However, feeling cold from being outside with short exposures to the cold weather with or without being wet or with or without a jacket does not produce hypothermia. Hypothermia is a medical diagnosis made by measuring the core body temperature which doesn't change in the cold without long term continued unprotected exposure to extremely low temperatures or without being fully immersed in very cold water.