> My thoughts are that a bottom entrance as big as the top entrance
 > should be ok for exchange of air.

Maybe, but on warm days, the condensation ice melts and runs to the
floor.  A closed entrance keeps moisture in and it evaporates back up
again.  With an open  entrance, that moisture dries out better.

Also warm air on warm days enters better with an open entrance and
warming is generally good. The cool air on cold days does not have much
effect on a tight cluster unless the hives are exposed to wind in which
case some entrance restriction may be wise.  Shelter would be better,
though.

It is important that all the hive openings be on the same one side of
the hive so that wind does not blow on and through the cluster.

As for bottom space, in summer more than a bee space below may result in
comb on the bottom of frames, especially if th3e beekeeper crowds the
bees by supering late, but in winter, dead air space below is very
helpful to allow the entering air to mix and reduce drafts as well as to
isolate dead bees from the cluster. An empty super with or without
frames raises the hive off the ground (good) and supplies air space,
plus spring expansion room.  I use a normal brood box with feed under
and the improvement in wintering is visible.

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