It is permissible to pray with nail polish on, but nail polish prevents water from reaching your skin. It is, therefore, a must to remove the nail polish before making wudu’.
Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states: It is permissible to pray with nail polish on, but it is worth pointing out that it must be removed before performing obligatory ablution.

For one of the absolute requirements for the validity of ablution is that water should come in contact with one’s skin (unless of course one is suffering from a medical condition that prevents using water). Since nail polish has a thick layer of coating that prevents water coming in contact with the skin, wudu’ performed while wearing nail polish shall be considered as null and void.
Having said this, we must say once wudu’ has been performed, applying nail polish does not break wudu’. But it goes without saying, in case wudu’ is broken and it becomes necessary to redo it, one must remove the nail polish again before performing wudu’.
If after removal of the coating of nail polish, a slight colour remains, one need not worry about it, for that is excused.