My trail mare drives me crazy with fear too — she used to not drink away from home. At all (not even in streams). But like some others suggested above, I have always traveled with buckets of our own water — in food grade buckets is important (so they don’t taste like plastic by the time I open them!) — and I switched the water bucket I use in her stall to a small, over the rail portable one, and take that with me, so that she is familiar with it and its smell. That has been the only thing, it works better than anything else I have tried (including the soda and horse quencher suggestions, which my mare just turned her nose up to). It’s a RELIEF to finally know she’ll drink!