Hive type is irrelevant. Wood or poly. Mice do not, except in very rare cases, go in through a 3/8" entrance. All our hives are on that depth of floor and we never get mice inside via the front door. The least secure material appears to be cedar, pine and poly less so, but to get it in perspective we are talking maybe a dozen hives over 20 years invaded by mice by this route........so about 1 in 3000 hive winterings.......not worth the bother of using mouseguards.
Most continental hives have had this taken inot account in the design of them, hence PH's observation about the German ones. they seem to be all like that.
On the contrary however are the deeper entrances used in this country such as on Nationals, which are virtually an invitation to free board and lodgings for the winter to mice.
In several countries you get reversible floors, with a deep side and a shallow side, and if you are so minded you just turn the floor over ( actually they usually are front or backso you also have to rotate it through 180deg) and then you have an unobstructed 3/82 floor for winter and a full depth entrance for the hot conditions in summer. We just use the 3/8" side all year, as do most bigger outfits I know of. Mouseguards not required.
Shrews are a different thing and some see them and think it to be mice........usually do a lot less damage as they can live happily betweeen two frames and just shave both sides back to the foundation, and the bees fix it up just fine in spring. They CAN go in a 3/8" entrance but we think of them as largely benign.
Elsewhere someone mentioned the effect of leaving a flat piece of equipment lying around and lifting it up after a couple of weeks and seeing the holes and runs underneath. This is true, but the culprits, if culprit is the right word, is usually the field vole, and those are completely harmless to us and our hives.
We DO sometimes get a mouse in though, defective hive parts or careless placing of feeders etc, or dislodging by things bumping against the hives are the issue there. Occasionally we find that an old non standard floor has been taken out of the shed and they too can get mice inside..........most have been burned by now and will have a final cull this winter.
