I'm not aware of any power that would allow a parish council to prohibit horses on a village green. The usual way in which a local council implements a legal prohibition is by requesting the principal authority (usually the district council) to create a byelaw. The principal authority's legal officer would have to consider whether a byelaw was feasible in any particular case. If there is a conflict with grazing rights, professional advice may well be needed to reach a clear position, either through the principal authority or otherwise.