You know, lots of people describe thrush as black and oozy. But by the time it's at that stage, you should have noticed it. OP, I suspect you have caught it long before it gets that far. - good for you.
Yup, keep those feet clean and as free of the muck as you can. I know it's hard. Wash with lysol or sunlight dish soap using a stiff bristled brush. Some athlete's foot cream helps, but if you have really wet fields right now, a commerical product may be called for as it will adhere better.
Also, keep the hooves well maintained. If your farrier hasn't been out in the last three weeks, get him/her out ASAP. Then (s)he can advise you on future care.