I believe you are referring to composting horse manure. As far as composting goes, it makes only a subtle difference whether you use wood or straw, both are carbon sources. Good mixing, moisture control, oxygen, and carbon to nitrogen ratio are key to getting manure to compost. With a little experimenting, it is easy to figure out how to do. The sawdust has an advantage in that it is easier to keep air in the system than straw. Therefore you will need to turn the pile more often with straw.

Exact ratios of manure, straw, and sawdust are best discovered on your own. If heat is generated (120 deg F) then it worked, if not then try another mixture. Typically with horses, depending upon how you manage your operation, I have found most have much more bedding than they need to compost. You may need to find a way to remove some straw/woodchips/sawdust before you go to your compost pile.

There are several good factsheets on composting and horse manure management on the small farms factsheet series on e-extension. I would suggest perusing them.

Here is one.