Buttercups are toxic to horses and other animals. Overgrazing is the root of the buttercup problem on many farms. Before the grass gets grazed down to the ground, move horses to a different field or use temporary fencing such as electric tape to section off rotating parts of the pasture to let the grass recover.
Source: Horse Channel, May 5, 2017.
Horses generally have no interest in grazing on them when other food is available, and they are adept at eating around them. But they survive in a horse’s teeth and when everything else around gets grazed down, they can thrive and spread. The best way to control buttercups is to think ahead and start managing your pastures months before buttercups appear and bloom in the springtime.