I know the wet cloth thing is supposed to help, but I've actually never done it, just never think of finding an older large sock to use for this.
would like to try it to see how much it helps on a stinking hot day.
I do think I'll pass on the underwear though
I find that just a plastic bag or two can help a lot. And a plastic bag fits much better in a cage than a sock. The plastic bag(s) reduces how fast the water warms up because the air flow past the bottle is minimized when the bag traps static air inside.
I discovered the plastic bag for cooling by accident. I wrapped a plastic bag around a bottle to put in my under-downtube bottle cage when riding on a muddy day to keep the bottle clean. And the bag appeared to help keep the bottle cooler.
I usually do not bother trying to keep my water bottles cold in hot weather if it is just water. Drinking warm water does not bother me on a hot day. But I insist on using a vacuum insulated stainless bottle for my iced coffee.