Welcome to HSO!
I didn't learn how fun ice-fishing was until I was in my early twenties and living in Winona. You may want to check out the Ice Fishing forum here for some good advice on gear and such.
Anyhow, Bartlett Lake (actually a backwater), known locally in Winona as the "Airport Lake", is still a good place to catch numbers of sunfish.
You may also try east Lake Winona, which I hear has become a much better fishery than it was in the '90s when I lived there. DO NOT go too near the aerators, due to thin ice.
There are plenty of other places to try around Winona: Sam Gordy Slough, Schneider Lake, the Minnesota City Boat Harbor, and McNally Landing (although that is better at first ice), to name a few.