We usually have a couple of snowstorms a year. Plowing will depend on amount, but it should be much less than northern Illinois, I think. And maybe an ice storm at some point. As for cold, maybe once or twice a winter, it will dip to 0 or shortly below overnight, but mostly winter = 30ish. The thing I like about southern Missouri is that when it does snow/dip, it never stays there. You will have a bad day, then the yo-yo bounces back. Very odd to have something settle in for days and days and days. I lived in Minnesota for four years, where snow and cold did settle in for the long haul, and I appreciate Missouri’s version. You wave at it as it drives by, but it will not set up camp for the season.
As for vets, Columbia is excellent. There are few equine-specific vets out in the rural areas. Most likely, you are going to be getting a “we see everything, large and small” practice for routine stuff and haul to Columbia if you need something major. There is a repro vet specialist in West Plains.
Cost of living is low, and while we have four distinct seasons, winter isn’t too bad. I like it.