Praise be to Allah.
Shaykh ‘Abd al-‘Aziz ibn Baz (may Allah have mercy on him) said:
“It is proven that the Messenger of Allah (peace and blessings of Allah be upon him) said to al-Laqit ibn Saburah: “Do wudu well and make the water go between your fingers, and be thorough in rinsing the nose, unless you are fasting.”
So he (peace and blessings of Allah be upon him) told him to do wudu well then he said: “…and be thorough in rinsing the nose, unless you are fasting.”
This indicates that the fasting person may rinse his mouth and nose, but he should not be too thorough in doing so lest the water reach his throat . As for rinsing the nose and mouth , they are essential when doing wudu and ghusl, because they are obligatory parts of those actions, whether one is fasting or not.”
And Allah knows best.