I find that a standard rigid mtb is the best for snow/ice. The geometry of a cruiser, with the weight shifted towards the back, makes the front wheel tend to wash out. The wide nokians should be ok for grip in snow. As you've noticed, the wider the tire, the more work you have to do to push them through the snow.

You might try switching out the super tall cruiser bars out for some mtb risers- would get your weight forward, and allow you to stand up a little more. A larger rear cog, for a lower rear gear, also might help. I run a 42X20 winter gear on 26" wheels.

On deep snow, if you have a low gear, and just keep pedaling, you can just power through some pretty gross stuff- the forward momentum gives you time to get the front wheel back under you.