Uh, snow is NOT "always 32 degrees", not by any means. It can get just as cold as the air does. (e.t.a. - perhaps you were thinking of ice-water, of which that IS true?) Because of its high air content though snow is still a good insulator even when it is pretty darn cold. So yes, piling it up against the sides of the coop does provide some insulation (until and unless you get an air gap developing between snow and wall, anyhow, which tends to happen)
Bagged leaves are also useful but can farm up rodents so should be used with thought and observation.
None of this is highly relevant to a slab though (as opposed to concrete or cinderblock kneewalls)... it makes a *little* difference if you insulate around the edges but really not *much* and there are far more useful things to worry about IMHO.
There is no reason not to build onto the existing slab, slab is a GREAT coop flooring. Just bed it real deep with fluffy shavings or fluffy straw in wintertime is all, and it works wonderfully. It is best to not leave any slab sticking out beyond the walls of the building -- i.e. try to use the WHOLE remainder of the slab for your coop -- because otherwise it can be hard/unreliable keeping rainwater that pools on the exposed slab from tracking into the coop underneath the walls. You may not have noticed this in your existing shed but you would sure notice (and care!) if it happened in a coop, as it'd result in damp bedding and frostbite type problems. There are things you can put under the sill to try to seal it but they do not always succeed so it's really better to try to avoid the situation in your design.
Good luck, have fun,
Pat