Sounds like a good plan. The only thing I can think to caution you on is to make sure the bedding straw, which you are using to cut down on weeds, doesn't contain horse manure, as quite a bit of seed can pass through an animal. In a compost pile, the seed are generally sterilised by the pile going in and out of a heat cycle. If there is manure in the straw, any seed in the manure will probably still be viable.

