My mother insists that I should put some oil on my baby’s back and chest before bath time. She said it will help baby not to get “cold”. Do you practice the same thing?

No. I never heard of this practice. I don't think it's advisable as the oil may get into the bathing water or baby's eyes while bathing. I think the best way to prevent baby from getting cold is to make sure that the bathing water is luke warm and baby is quickly wrapped in towel when he/she gets out of water. Also make sure the baby is dried thoroughly and dressed in warm clothes.