If hot liquids increase mucus velocity+inflammation, and cold liquids decrease mucus velocity+inflammation, wouldn't cold be better for post nasal drip cough and inflamed/sore throat?

Smile: That would be true if you are only flushing the mucous. You are using the fluid to be absorbed, delivered by the blood to the airways to liquefy the secretions. If you use cold on the nose, it causes vasodilatation and more congestion. Example try to put your face in the refrigerator and you get congested.The physiology of the body is not a 400 word lesson, so it is difficult to explain here.

Post nasal drip: Usually war, fluids are more effective to relief symptoms of sore throat, congestion and post nasal drip.

No: Cold fluid would not feel better if you use it for nasal irrigation to alleviate postnasal drip. Choice between cold and hot is based not on any scientific ideas, but rather on the level of comfort one or the other brings. In cases of inflammation it is recommended to avoid extremes - cold and hot and stick with the middle ground - lukewarm.