Re: dilapidated horse step
If you have access to a pressure washer, I would start by giving the area a very aggressive washing in an attempt to break away any loose paint. Depending on how good you want this stoop to look, you can strip it with a stripper made for concrete. Behr makes such a stripper made for garage floors. It is water rinsable.
For a finish coat, you can use an acrylic porch and floor paint or, a solid hide concrete stain. Concrete stains tend to penetrate deeper and do not leave a heavy coat on the surface, making it less likely to peel in the future.
All quality paints/stains will have a mildecide built in, but you can buy additives to hedge your bet if you wish.
I dislike glossy finish porch and floor paints for exterior use. They are just too slippery when wet. If you go that route, mix in fine silica traction sand. Any paint store will have such an additive.