I LOVE the gate!! Added that picture to my idea files :)
The "rag rug" out of hoses looks really interesting too, I may make one and see how it works for padding and traction. Rag rugs take forever to dry in my current climate if you let them get wet.
"Hose mats are very portable and stackable steps that can help us not to slip in the coming muddy times."
If a "bumpier" mat is acceptable, perhaps a framework of hose 'spokes' could be woven so that portions of the spiraled hose mat would become a 'knob' on the underside of the mat, much as a wicker basket would be constructed, except without the sides. Knobs would keep the mats from being moved around in high-traffic or heavyweight, damp areas like paddocks.
Using a soft collapsable hose for the spokes would make the job easier. Heating the vinyl hose at the weave-point. with a hair-dryer to soften it during weaving.
The 'depressions' caused by the hose could be filled in with dirt or clay.
"How to wind it, but I wonder if there's something more eco-friendly than zipties to fasten it together?"
You might try using plastic produce bags, twisted into a string, half-hitch knots to keep it all tight using a basket-weaving technique to use plastic-bag string 'spokes' that weave the hose together.