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I went to Michigan Tech for a few years. You'll quickly notice that people dress to stay warm and don't give a shit what they look like, so get whatever you want.
I wore some Merrell shoes with Gore-tex and vibram sole, kept my feet nice and toasty and dry and grippy in the snow. If you're just going to class, you don't have to dress too crazy. Like others have said, get a good hat, some gloves, and a normal winter jacket (no need for more than one). If you plan on spending some time ice fishing or skiing, then I'd get some thermals and better socks.
There's a decent amount of Freshman that transfer after their first year because they can't handle the winter. It will be a shock to somebody from the south, but it truly is amazing if you embrace the snow. Make sure you go to Winter Carnival in February in Houghton.