Well rotted horse manure, as long as the horses were bedded on straw, is the ideal manure - bulky and reasonably nutritious. Chicken manure can burn plants unless it's very well rotted - this might be partly because the urea component is a solid rather than a liquid but I am just surmising here. Also, not being great grass eaters, chicken manure is very concentrated - the bulk of horse manure is from all the hay etc they eat.
If shavings are used as bedding the result will take a long time to rot down sufficiently well that it will no longer remove nitrogen from the soil in order to break down further, so straw is far better as it will be well rotted down in a year.
We use sheep manure as we don't have horses and it is fairly similar. We rot it down separately from the chicken house cleanings so we can judge when each is ready but we use the two in a fairly similar way, rotavating it into the soil. Compost made from plant residues only can be safely used as a mulch around plants.