Nelie,
I don't find it a big problem. If I am at the gym on an aerobic machine, I get a foam cup of icewater with a lid and straw and put it in the holder, and sip from it as needed. If I am riding a bike or snow skiing, I use a Camelbak hydration backpack and sip from it as needed. If I am doing something less strenuous, like walking or playing golf, I just carry a bottle of water.
The problem for me is not the dry mouth, but getting the motivation to get to the gym!
Take care,
Danny G.