My top recommendation would be southern Spain (not the little beach towns, the great cities like Seville, Cordoba and Granada). But I imagine you've already been there, or it would be on the list you presented.
My second recommendation would be Sicily or Puglia.
When I'm trying to decide whether temperatures are likely to be acceptable to me at a potential destination, I use timeanddate.com to find actual, historical, day-by-day weather data going back about ten years. For precipitation data and average hours of sunlight, I take the easy way out and look at the Wikipedia entries for places I'm considering. The climate chart usually (not always) has monthly-average precipitation and sunlight statistics.
MIlan weather -- February 2022 << Use the pull-down box to change the month/year.
Your odds are better south of the Alps, but I wouldn't go to northern Italy in the winter. Then again, I've been to the Twin Cities several times in January, and I understand where you're coming from (both literally and figuratively).
Edited to add: In cities such as you list, I wouldn't expect issues with closures, though you might run into the rare minor sight that closes in the winter. I've seen that for a few sights in Estonia or Latvia, I think.
I took my first winter trip to Europe this year--to Rome, Naples and Salerno in February/March. The weather was well within the range historical statistics suggested--perhaps a bit warmer and with less rain. What I hadn't really expected was that on many days the temperature didn't get up to 40F until 11 AM or noon, even when the high temperature ultimately got way up into the 50s or lower 60s, so I had to bundle up when I headed out and then peal off layers as the day progressed. Of course, it got dark very early (expected), so I was returning to my hotel every night in the dark, which was a safety issue--not because of crime but because of rough sidewalks, sometimes ill-lit. The latter was an unexpected side effect of traveling in the winter.
The only closures that affected me were those involving cafes at some of the smaller museums. They were often closed; I had the feeling it was just for the off-season, not a post-COVID, semi-permanent situation.