In general, horses will avoid plants that are poisonous, provided they have adequate sources of nutrition. It is always best to avoid planting poisonous plants where horses can access them even if it is only occasionally.
Clematis contains irritating substances that cause mouth irritation, excessive salivation and diarrhea if eaten in quantity. Excess diarrhea can lead to dehydration, which can lead to more serious health issues. There is no readily available information on the palatability of clematis. The plant contains irritants whether it is flowering or not.