Praise be to Allah.
It is permissible for a woman to colour her nails for the purpose of adornment, with materials that do not cause harm, and there is nothing wrong with her praying with that, unless it is a substance that prevents water from reaching what is beneath it, in which case wudoo’ and ghusl are not valid unless it is removed. If the wudoo’ is not valid then the prayer is not valid.
It says in Fataawa al-Lajnah al-Daa’imah, 5/218:
“If the colour is impermeable, then wudoo’ is not valid unless it is removed before doing wudoo’. If it is not impermeable, then wudoo’ is valid, as is the case with henna.”
And Allaah knows best.