Boots?
My sadly deceased Holsteiner had the worst feet in the world so we had to stop shoeing him so he wore Boa boots all round for 3 years. I liked them, on the whole, but they are advertised as non-slip.... not so. They are OK'ish on slippy surfaces but no better than shoes in my experience.
So some form of stud might be your only option.
How very annoying