Depending on condition of the wood, I'd remove them from the ladder itself, sand and re-stain them and them epoxy them completely.
I wouldn't use epoxy unless you cover it with a UV protectorate layer that will bond with the epoxy. Also, if you stain the wood below, you'll need to have something that will bond with the epoxy.
One "short-cut" that some people use with varnish is to use a layer (or two) of epoxy that is put on lightly sanded, clean wood; and then sanded lightly itself before putting a couple layers of varnish on top of that. That works best inside the boat -- but if you use a exterior grade, marine varnish, with UV additives, it can work outside.
I'm not sure are bout "grit" for a variety of reasons as a non-skid.