Is it just horse droppings or is it bedding? If bedding, what does it contain - wood shavings or straw?
Horse droppings don't tend to burn like chicken droppings, although it's best not to use it touching plants. I have rotted it down in bags, tied up and placed in the sun. I have also spread and covered it as Rosemary suggests.
However, if it contains wood shavings then you need to rot it down for a year, otherwise the decomposition of the wood will deplete the soil of nitrogen.