What would the water table be at for natural vegetation? ie what is your woodland like. Water table is water table.Obviously it does work. What I mean is that trying to achieve infiltration doesn't work. Or rather, it doesn't here.
I've read all the books, seen talks about how Gabe Brown et al just get all the rainwater to infiltrate away in 5 minutes, and how valuable every drop of that water is, and I regret spending so much time and money thinking I could achieve the same thing.
Dig down a foot or two anywhere here and you find solid clay, which water can't infiltrate. We dug infiltration test holes when we replacing the septic system some years ago and the water didn't run away.
I've spent three years moving sheep and cattle around every day or two, and the fields are worse than they were before I started. It's like the _soil_ layer has improved, but all that means is that when it rains for days and days (and days) on end, I have a much bigger sponge sitting on top of the impermeable clay, so the fields are just so much wetter than before. Then even if it stops raining for a couple of days the fields don't dry out at all, because it's all just sitting in the soil.
The only way to improve anything is drainage. (Trying to achieve) infiltration is hopeless.
 obviously not all the books in the world. I was moving fences around too much for _all_ the books in the world.
Also this sort of grazing in the UK is about extending your winter and improving your summer grazing not eliminating your need for bringing stock in in the winter. Holistic Management principles would recognise this - no one size fits all.
Every farm is different.