Don't you think you may have answered your own question?

Midwest, snow, salt, mud, rain...sleet......kids, big dog....

Please define nightmare. While it is true marble has been walked on for multiples of centuries? If you think you can walk right in onto those floors and not have a mop nearby? My answer is I doubt it: ) How many times will you wipe the big doggie paws? Are you good with a huge commercial walk off mat in charcoal or black?? You will need it.

Consider slate. A stone. It should be sealed (and resealed) before installation. But is a timeless look. And even so…will scratch, etc. It is dark enough so that you will see the salt crystals your boots will bring in. And the paw prints of your dog. And your kids will scuff it up. But that is all part of a Midwest lifestyle, no? (Trust me, I know.). Slate yes. HONED marble, heck no! Not even on my bathroom floor! Just one opinion.

Can’t comment on marble, but wondering if you have considered brick / a very different look, but if durability and maintenance are priorities, there is lots of on line pro’s/con‘s info (as well as for marble). Since marble is classic, you can achieve that with brick done in a herringbone pattern.

Porcelin non-slip with a marble look

We have a honed marble floor in our midwest foyer (still looks great @100 yrs) but I think they are other materials better suited for a mudroom - in my experience, the checkerboard is hard to keep clean - we had it in a kitchen years ago and the only time it looked clean was right after I cleaned it