the 1 kg will stay 1 kg whether wet or dry snow or water or ice or water vapor, as long as none of the weight is from dirt (not snow-ice-water). And even then, that weight would stay there unless you filtered out the dirt.
the problem with wet snow is its high density, of course. 6 inches of wet snow on the ground is one heck of a lot more mass than the same depth of that nice fluffy stuff we sometimes get. I shoveled a foot and half of dry snow last week and it wasn't super hard. Way better than a half-foot of wet snow. I hate shoveling wet snow.