What is the ruling on wearing a hooded abaya?

All praise is due to Allah, and prayers and peace be upon the Messenger of Allah.

To proceed: If the "hooded abaya" you are referring to is a head abaya, then wearing it is permissible; in fact, it is more effective in covering. It is obligatory for a Muslim woman to cover her entire body from non-mahram men with clothing that does not resemble men's attire, does not reveal the shape of her limbs, and is not see-through. If these conditions are met, there is no obligation to adhere to a specific type of abaya. And Allah knows best.