So, is it good to drink cold water when sick? The answer, delivered with a confident shrug, is: Yes, absolutely, unless it makes you uncomfortable. The only real enemy here is dehydration. Fight that demon with any temperature of water you desire. If cold water makes your teeth ache or your cough worse, switch to warm. But if it feels like a tiny angelic icicle rescuing you from the fiery pits of hell? Drink up, you beautiful, feverish mess.
In conclusion, the great cold-vs-warm debate is a distraction from the one true fact: just drink the dang water. Unless your drink of choice is a triple-shot espresso or a barrel of whiskey, in which case, please see your doctor immediately. But for regular H2O? Ice it, heat it, serve it with a tiny umbrella. Your body needs the liquid, and your sanity needs a win. Now go drink something. Stat.