Cloudy ice is a sign that the ice formed and then melted. There are going to be a lot of lakes this season that are more or less cloudy in their entirety due to the weather we've had so far. That ice is significantly weaker than clear ice. All the safe ice depth charts you see are based on clear ice, so keep that in mind when you want to drive your truck out on 12" of ice that is cloudy all the way through, as many lakes up here are.
Regarding the snow, it generally has an insulating effect which can make it more difficult for the lake to make more ice (clear, windswept lakes will make ice the fastest). It can also shield the existing ice from warmer weather...until it doesn't. Warm enough weather for a long enough period to melt the snow...or overflow from the weight of the snow itself...can cause water on top of the ice. However it formed (I would guess melting snow down south) that water and slush also ruins the ice.
TLDR: Snow on ice - not really a problem, but expect less ice on lakes with a lot of snow on them
Slush/water on ice - not a good thing for ice integrity and you might want to pause to ask yourself how it got there.
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