You can buy rubber safety boot covers at safety supply places (maybe Grainger.com as well?). I've seen thin ones and thick ones...go for the thick ones if you try it.
They won't hold up to rocks all day but as quick mud covers in dirt they should be fine. We used to wear them for hours doing environtal work on concrete, grass, jobsites, etc.
If you get the ones that go over your shoes, use plastic grocery bags over your shoes and the rubber boots slide on alot easier. Thats how we did it in construction pouring concrete easy on/easy off.