In my neck of the woods people love using decomposed granite which is probably similar to stone dust. You'll hear a lot of different terminologies depending on the area - most landscape material suppliers should know a popular option that other local horse owners use.
Mud will swallow most anything you put down so expect it to disappear and top it off as needed, or go all out and scrape the mud, add a membrane, and layer different stone sizes for drainage. A variety of materials can be good too - stone dust for hard-standing areas, a sandy spot provides a great rolling/sleeping area (or a toilet in my geldings' case), pea gravel is a popular option to stimulate the hooves for healthy growth and wear.
If you can't cover the whole dry lot at once you can just add materials in certain spots so she can choose to relieve herself from the mud. I have rubber stall mats at my gates and food stations, and pea gravel around the water trough. I've also heard of people using old carpet in a pinch - lay the carpet upside down so the smooth side is up to stand on.
