The easiest way to stop your ground being churned up by 15 horses is to put them inside once the weather turns wet. In this country large animals are usually housed overwinter not because they can't stand the cold, but because of the damage they do to the land.
I've had up to 15 donkeys at a time and found it SO much easier for us in winter to house them in our cattle building. It's not a lot of fun for the animals either, tramping about in mud.
We have them on a deep litter system where they are bedded down daily with fresh straw, then the whole lot is mucked out in spring, by tractor, when the animals have gone outside again. The other advantage is that you can spend quality time with your animals in winter - inside, in the warmth, and caring for them becomes a pleasure, not a chore.
No doubt your answer to this is that you don't have a suitable building - to which I would say "Well get one!" You can build a simple pole barn relatively cheaply and then improve on it as funds allow.
With 15 horses you are never going to beat the mud; even if you put a load of hardcore in your gateways each year. With 80 acres you can maybe move the animals round in winter as each area gets destroyed. But then you end up in spring with a total mess.