Several of us out here have used geotextile (not necessarily "cow carpet") for paddocks. I'm sure a search, as suggested above, will yield many of those threads.
For me, our paddocks were originally done with geotextile and then 8 inches or so of 5/8" minus rock, and another 2 to 3 inches of small pea gravel on top of that (probably 3/8" diameter, rounded rock). This worked just great with the retired horse and mini mule. The 5/8" minus packs pretty well, but still allows drainage, and the pea gravel stays loose so it isn't a flat, hard surface - great for feet.
Then I got the two year old warmblood who felt it was his life mission to dig up and retrieve whatever buried treasure was under the fabric. Holes dug everywhere, fabric torn up, etc. Since he was doing it, everyone else did it. I was so tired of filling holes. Especially when they poop, dig a hole, and what they dug up was flung on top of the poop...it was miserable.
So we redid the paddocks with Hoof-Grid -- basically took out most of the gravel we had to get a good, flat surface (there is still a lot of rock under there as we had drainage rock under the fabric, etc.) that still drains well, and laid the grids on top, then pea gravel in and over that. Love it!
Now, a different group of horses would be fine on the geotextile/rock set-up. In fact, my neighbor has this (copied ours after seeing how well it worked...before the two year old destructo horse was here) and it has worked out really well. I just have had these young diggers and done lots of lay-up for injuries (so confined and bored), so the hoof-grid stuff was a better plan for me. But more $$. Worth it, in my case.
Your area and land will differ, but the first thing I think is to make sure that water doesn't collect on the surface. Make sure no roofs drain into the area; raise or slope the grade so that water that falls on it doesn't collect. My soil can turn to muck and we get a lot of rain in winter, but the only places that are really awful are places where water can collect.
If you are allergic to a thing, it is best not to put that thing in your mouth, particularly if the thing is cats. - Lemony Snicket
Thanks all. I think for this case I will use a 6 oz equivalent (one oz less than Cow Carpet, but maybe from that same company) and put 6" of local natural stream bank class 6 road base on top, pack well, then either some dirt or squeegee if they will never feed on it. These are runs off of stalls and have good drainage, and the horses go out to pasture a lot (nice place). Owner just said she wants to do what is possible to eliminate mud. I will probably have some sort of french drain out from the ends of the runs where the horses turn around - where a swale always develops to not drain water that will freeze in winter.
I am wary of just gravel on top of GeoTextile, as yes, it would be easy to dig through. The local company that wholesales a 6oz non-woven needlepunched equivalent has a retail price higher than the price for the 7 oz Cow Carpet, so that seems to be priced fairly.