Curious as to why it has to move. Do your livestock have No legs?
Discussion
Livestock concentrate around stock tanks concentrating impact in that area compacting it. They also overgraze the grasses close to it.
If the stock tank moves around then so will the animals and they won’t overgraze around the tank and compaction will turn into widespread disturbance which causes new grass to grow.
It also would distribute urine and feces instead of concentrating it in one area.
Clever✅ now I think about it the area around our creek and dams where the livestock drank got really mucky in winter too.