I sniffed water into my nose, and later on when I swallowed some mucus, as it went down my throat, it felt like some of the water which I sniffed mixed with the mucus in my nose due to a cold sensation. Is the fast valid when this happens? (water mixes with mucus and one swallows that?)

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Your fasting is valid, and swallowing mucus or feeling the cold sensation of the water that you sniffed does not affect its validity, for two reasons.

1) Intentionally swallowing mucus in the way you mentioned does not invalidate the fast according to the view we adopt.

2) The remaining of water after being sniffed and it getting mixed with the swallowed mucus cannot be affirmed. Also, the cold sensations does not indicate the existence of water and, therefore, there is nothing that invalidated your fast. This is said based on the assumption that you deliberately swallowed mucus with the feeling of coldness. However, if you swallowed it unintentionally, even if water is there, the matter is easier and there is less room for disagreement among scholars.

Allah Knows best.