So, hunters carried 2-3 liters of water during hunting? Have you seen in the museums the water pouches made from leather? They barely hold a liter to a liter and a half. Even the ones I've seen made from wood barely hold more than a liter. I doubt people always hunted close to streams so that they didn't need to carry water with them.
Depending on where you live, you will sweat out a lot more water on a daylong hunt.
But in semi-arid climates, where streams are rare, animals tend to gather around watering holes, so that might actually be the best place to start your hunt.
