The "Wisconsin" dish in my opinion is Hotdish. In Western parts of the state it's Lutefisk. Feel free to google either for more detailed information
One thing to remember about Wisconsin... There's Madison, Milwaukee, and Everything Else.

Most of your average Northerner's have more in common with a Yooper than they do with the citydwellers.

After all Milwaukee and Madison are two of Chicago's largest suburbs! /joke.
Other answers to your questions:
1. Ladysmith is very small

There's one small movie theater in town. I think there's another even smaller one in Bruce, WI nearby. Most people I knew in Ladysmith just drove the hour into Eau Claire - shopped, ate and saw a movie and made a day of it there instead.
2. The best things to do in smalltowns are generally City Baseball games, and Highschool Football games. Hunting is a VERY big activity. So is four-wheeling and snowmobiling.
3. The main roads are generally plowed on the weekdays when it snows in smaller towns, and yes they're very good about it. The only time it usually lacks is if it snows around 4-6 am before the plows really get a chance to hit alot of the roads before everyone goes to work. In my humble opinion, North of Hwy 64, four-wheel drive is a requirement. So are engine block heaters if you park outside.
4. Other things to do: Hunt, Fish, Boating, Ice Fishing, play cribbage. Most of everyone will goto the local watering holes (Bars) Friday's and Saturday's.