Slush has little to do with ice safety. The ice is not a bridge from bank to bank, it is a raft. Ice is about 8% less dense than water, so it floats, about 8% out of the water. 6 inches of ice with no weight on top would float with the ice surface about 1/2 inch above the water surface. If you stand on it, it bows down slightly, and that half inch is slightly less. If you put a foot of snow on top, the weight of that snow will push the top of the ice under water. Water will come up through every crack and hole, and make slush. Eventually, the snow will settle and the slush will freeze into “white ice”, and become part of the total ice thickness, and you can walk on that new surface.
As someone also stated, there is a point where the top of this new surface freezes, and the underneath is still slushy, and you get layers of crust and ice, but the original 6 inches of clear ice is still there, and melts extremely slowly, so unless you are near springs or warm water, it is still safe.
Out here, the larger concern is going to be the shore edges rotting as the snow melts on shore, and boat ramps and streams melting the clear ice from underneath.