The best way to figure out what something would be like, is to look for parallels in the modern-day world. In this case, you're looking for a mid-latitude inland location not too far from a polar ice cap. That's something of a problem here: the edges of both polar icecaps are on coastlines, far from the mid-latitudes. So, I'm going to fake it with a hybrid of Fairbanks and St. Louis, with bit of Thule Air Force Base thrown in for cold.
St. Louis is far from any large bodies of water, so you're going to get wide temperature swings, both day-night and summer-winter. In the summer, you can expect high temperatures above 50F (10C), with overnight lows usually above freezing. Warm spells of up to 80F (25C) won't be unheard-of. In the winter, high temperatures will usually be around 0F (-20C), with lows around -20F (-30C). During the November-February period, temperatures will almost never rise above freezing, and spells of bitter cold hitting as low as -65F (-55C) will be possible.
Between the low temperatures and the inland location, it's going to be dry. Contrary to the popular imagination, you won't get much snow in the winter: the air can't hold much moisture. Most of the precipitation will arrive during summer, and it won't all be rain: it can snow on any day of the year.
The cold winter temperatures mean that you'll get a shallow-lying layer of permafrost. In the spring, snowmelt won't soak into the ground -- it's got nowhere to go. Instead, you'll get mud and small ponds all over the place, with the corresponding swarms of mosquitoes.
The geography of the area makes the Mississippi riverbed a natural drainage channel for meltwater from the glaciers, but the river will be just a shadow of its former self. The river will freeze in the winter, with breakup (and possible ice-dam flooding) in the spring.
Your outpost will need to get most of its food either from imports or from hunting, possibly supplemented with crops grown in greenhouses. The possibility of frost at any time greatly limits the possibility of large-scale outdoor farming.