I recommend getting a metal water bottle and carrying that around when you’re sightseeing or any activity that keeps you outside in the sun for long.
Also I personally never noticed any extra sweating when drinking cold water versus ambient temperature water, and I live in Portugal were we regularly get 40C or more in August. Generally, if it’s hot enough you’ll sweat more simply from the heat (as sweating is a natural cooling mechanism) even if all you drink is plain tap water. Sure, if you don’t drink water you’ll sweat less, as you’re getting dehydrated so the body will cut down on that.
Were did you learn that specific piece of information about cold water making people sweat more?