I always travel with full water.
1) I know its good water. Campgrounds on wells may taste fine but could still introduce microbes to your water system
2) I don't have to waste time looking for and filling the tank on the road.
3) I have water in case of emergency (i.e. getting stranded for extra days due to snow, or in the summer due to forest fire closures).
4) My trailer tows better with full water. It's basically 800 pounds of ballast sitting over the axles. I notice more side-to-side motion of the trailer with high winds if its empty.
2000 Ford E450 V10 VAN! 450,000+ miles
2014 ORV really big trailer
2015 Ford Focus ST