I've spent a few weeks in a place with no hot running water before (only a "shower" filled with water from a meltwater river and the river itself), so I can comfortably say that you can indeed get perfectly clean with one of those. It's mostly a function of the amount of time you're willing to spend in there.
i get clean enough for my needs, which might be different than yours. I find that hot water is only really necessary to get rid of stuff that's stuck which is not a very frequent thing, but if you don't agree you can always combine hot and cold