I would talk to the DNR about Trail Crossings on water. The Trail Ride folks are working with The Parks and Recreation folks in many areas to keep horse trails usable. There are MANY acceptable ways to increase safety in good footing, prevent making the water muddy downstream, yet not impede the flow during all seasons. Ways to help KEEP the footing in place during strong run-offs! There must be some books or articles about how to build, maintain, or keep these kinds of water crossings working for horse folks. You might ask this question again over in the Endurance and Trail Riding Forum. Lots of knowledge over there. You might want to post your location, water works differently in various locations and state settings for runoff or severity of your weather. Locally we get LOTS of water, heavy runoff after storms, but with mostly gravel bottom creeks or rivers, the footing under the water is not a problem here. No mountains to hurry the flow either! So our ideas may not work at your farm.
Probably what you would be most interested in would be a Fording type crossing, where you just go thru water on good footing. No blocking the water at all, to make the DNR happy! I am going to say that rocky gravel or crushed stone would be the choice to put down and expect it to stay mostly in place. Wood is VERY slippery when wet or left in running water. Gets even slipperier with green stuff growing on it. Not good for the base of a crossing! I have clay dirt and see it only being VERY SLIPPERY any time it is wet. Can’t think clay would stay in place against a running water force. Rock is still going to let wheels sink in a little, you can’t pack it down hard in running water. But no clouds of dirt going downstream, something firm to let horse keep their feet from getting stuck in, while going thru. But how you put stone in the crossing, spread it out, what depth, “soften” the water approaching it, will help keep it in place over the long run for using the crossings. Chunky rocks are harder to move usually, crushed gives sharper edges to bind them together when pushed than the rounded gravel stones.
Those are my best ideas!