Praise be to Allah.
It is not obligatory to remove earrings or nose rings that women wear for adornment, either when doing wudoo’ or when doing ghusl. Rather it is sufficient to wash the outside of the ear and the nose, for the following reasons:
What is required is to wash the outside of the nose (which is part of the face) when doing wudoo’ and ghusl. As for the inside of the nose (which includes the pierced hole where the jewellery is placed), it is not required to wash it; rather what is required is to take up water into the nose and expel it, which can be done with this pierced hole and with the jewellery in place, so it is not essential to take it off or move it.
In the case of the ear, it is not required to wash it when doing wudoo’; rather it is recommended to wipe it, and the part of the ear that it is recommended to wipe is the auditory meatus (the external auditory canal) into which the forefinger is inserted, and the outside of the ear is wiped with the thumb.
With regard to the place that is pierced in order to wear earrings, it is not recommended to wipe it when doing wudoo’, hence wearing earrings makes no difference with regard to the validity of wudoo’, and it is not required to move the earrings or take them off.
With regard to ghusl, the ear is to be washed like the rest of the body, and the hole for the piercing is overlooked according to the Shaafa‘is, so it is not required to make the water enter it, because they regard it as being part of the inside of the body and not part of the outside of the body that must be washed.
It says in al-Mawsoo‘ah al-Fiqhiyyah (13/19):
The scholars are unanimously agreed that it is essential to make water reach whatever it is possible to make it reach of all parts of the body, even if they are sunken, such as the inside of the bellybutton, and the sites of surgical procedures which have sunken scars.
But the Shaafa‘is regard the pierced hole of the ear in which earrings are placed as being part of the inside of the body, not the outside, so it is not essential to make water enter it, even if that is possible. End quote.
And Allah knows best.