No I don't think it is common thermo- wise to carry water around.
I don't want to sound churlish, it's just that women have fought so hard for breastfeeding to be "normalised" that many don't want to be singled out as something unusual. If you know you get thirsty while breastfeeding then carry extra water with you.
A good cafe should be helpful to all its customers, whether wheelchair users, someone who struggles to read the menu, a busy Mums with children, an elderly person who struggles with their seat etc, it's part of being a good establishment.
As good intentioned as the OP is, I could just see this backfiring.