> The question is not how much you see on the upper entrances but how much ice you see under the inner lids and on frames.  

Yes exactly - among the USA hobby beekeeping crowd, "inner covers" are used, and the cheap ones are pine frames around a sheet of Homasote (fiberboard).  This sort of inner cover can become very waterlogged, but they do prevent small amounts of moisture from dripping down on the bees, as even if the conditions allow for liquid water, the Homasote is very absorbent.

The Germans and many other Europeans put a sheet of thin clear plastic across the topmost box to prevent the bees from propolizing the lid too badly - they might be a better source of data on the issue, but their winters are fairly mild.
 

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