Possibly Aiyanar, a village "watchman" deity usually on horseback

When one travels through South India, terracotta (or other materials) horses can often be seen in the middle of a field, with out without a rider. From several thousand years back, in Tamil Nadu, big monolithic ceramic sculptures have been built as gifts to the god Aiyanar. 
Aiyanar is the hindu village protecting god and the sculptures are often images of horses, sometime more than 5 m high, built in one piece and fired in situ.
The horses are to be used by Aiyanar and his men, when riding through the village by night, protecting it from fire, thieves, drought and illness.