CaptainCompostAL is correct - not best for spreading directly on your garden.
HOWEVER, stable clean-out is REALLY good stuff - but, you will need to learn how to best handle it. Will need more detailed infomation, so if you don't mind answering some questions?
1) How is the stall material is loaded onto your vehicle or trailer - tractor bucket, or shovel by you?
2) How often is sawdust spread into the stall - regularly or intermittently? This has to do with how well manure is 'trampled' into the sawdust by the time you harvest the material, and whether the horse(s) get a regular diet of sweet grain or other commercial feed (manure content).
3) What kind of wood is the sawdust from (oak, pine, cedar, etc.)? Is it from a consistent source? Is it chips/shavings, or actually saw dust?
4) How often can you 'harvest' this stuff regularly? Is it free?
5) Do you have a non-chlorinated source to water with?
6) What type of pile do you normally build (wire frame, solid bin or frame method?
7) Do you own a 20" compost thermometer?
8 ) How often do you turn/water your piles?
9) Do you collect compost 'tea' when watering your piles?
If mostly sawdust, it is best to put this stuff into a separate pile, to 'age' with addition of Blood Meal (12-0-0) mixed into it (as the material is loaded and again as you unload it) to do the mixing without additional effort. How much blood meal per load is determined by how fresh the manure is in it, and what percentage (estimate) of sawdust is in it. It's an "experience" thing. A different "set" of microbes decomposes woody materials (cellulose/lignin) than decompose leafy materials, but IF you regularly have green material (such as freshly-aged grass clippings or fresh cow manure) on hand that can be added to the 'sawdust mix' as it is unloaded, then that's a whole different situation - so maybe then it would be good for building a 'regular' pile...?
Your answers are relative to adjusting the 'regular' pile 1st-heat temperature properly, which might indicate addition of a sugar/starch amendment, since pile heat is mainly caused by thermophyllic fungi 'eating' the initial available sugars and carbohydrates from the material you build the pile with. High-carbon materials are usually deficient in sugars/starches in a form that heat-producing fungi can assimilate.
You can incorporate an alternating layer of a very high-carbon mix into a 'regular' pile as you would an alternate layer of dry leaves - but how much, depends also on what your 'regular' carbon/nigrogen pile materials are.
Second focus would be on what additional material would need to be added during the 1st turn, to 'round out' the pile material to obtain a 2nd heat, and to begin maximizing production of humus percentage.