The main function of clothing is to hinder the flow of heat. The last thing you want to do when putting people into cryogenic sleep is to hinder the flow of heat. Quite the opposite: You want to have perfect control of the temperature on the skin.
So, you say, why not put on some special clothing that conducts heat well? Well, the insulation effect is not just coming from the clothes material itself, it also comes from the air it encloses. When you enter the cryogenic tank with your special tank clothes, it is almost certain that somewhere there will be a pocket of air that's caught in the clothes and not driven out by the cryogenic fluid. And that will insulate you.
OK, but what if you find a way to reliably get all air reliably moved out completely, so your suit is completely filled with cryogenic fluid? Well, the most efficient heat transport mechanism is convection, and that is what the cryogenic chambers will use as well. The clothes will prevent that convection to reach your skin, and therefore the cryogenic substance in between clothes and body itself will act as thermal insulation. Note that on normal use, also the air acts as insulation only because it is held by the clothes.
Well, OK, so let's make an elastic metal body suit that's actually "vacuumed" directly onto the body, with absolutely nothing in between the suit and the skin. That should finally work, right?
Well, probably. But I'd expect that experience to be so unpleasant that you'd really prefer being naked.