Living this far north my whole life I've learned a little bit about winter. Here's the 7 commandments of what not to leave in your car on very cold days.
Snow in South Dakota is not abnormal. October snow in South Dakota is not normal, but it isn't shocking. It doesn't happen every year, but it is a thing that happens. Snow will fall, it may or may not stick to the ground, but it usually doesn't hang around very long. But every now and then it does.
Depending on what half of South Dakota you're in, the winter could be either very snowy with storms, or not too bad. At least according to this 230 year old almanac.