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If you're handy you could easily make a nice shanty with some plywood and a tarp where it folds up real nice, that way it's easy to transport and drag around. Unless you only plan on going out for an hour or so a shanty is a must. All you need is a little lantern to heat it up real nice, whenever I go out I always end up sitting in just my T-shirt and pants all day, that's how easy they are to keep heated. Going out there with an axe is probably the dumbest thing I've ever heard. I'm trying to be nice because you're inexperienced but god damn whoever gave you that idea needs a slap on the head. Get an auger.
I don't know what kind of area you're in or what you're trying to catch so I can't give a lot of advice on bait. I live in Ohio and I usually fish for crappie in the winter, for ice fishing I only use maggots and I usually set my line pretty deep.