Bathing your baby when he or she has a cold is perfectly fine and the bathing will not cause the baby to become any sicker.
Although we were told by our parents before that having wet hair or going outside in the cold and getting wet can cause a cold that's not true.
Colds are caused by viruses so it's okay to give your baby a bath when it has a cold and the baby may actually feel better when you give him or her a bath when they have a cold because you could be washing off the germs that are living on your baby.
Just be sure to not let your baby get too cold though when giving them a bath and make sure the bath water is warm enough and your baby will be just fine.