Mid-September being 14-15 SEP? That leaves you two weeks, more or less, to accomplish your list. This can be done.
Starting in Stuttgart you have the MBZ museum and Christmas markets right there. You can easily do the museum in the day and the markets in the evening. But skiing, sledding, etc. are going to require you to go further south. I’d look at two specific areas; Bodensee and Garmisch-Partenkirchen.
Bodensee is little more than an hour south from Stuttgart, but you want to head to the south, Austrian, side of the lake. There are a couple ski resorts outside Dornbirn, not huge, but if there’s snow you can get your downhill time in. Plus you have Zepplin rides over the lake, Meersburg castle, Christmas markets in all the small towns around the lake and in Konstanz. And Zurich is less than an hour away by train.
Garmisch-Partenkirchen is a world class ski area; they’ve hosted the winter Olympics there. They have slopes for everyone, cross country, sledding, snowshoes, etc. And the places for gear too. Plus you have a number of the more attractive old towns that draw tourists from around the world (Oberammergau, Füssen, Mittenwald, to name a few). And Munich and Salzburg are an hour away by train. And you can, of course, see the castles…
Now, as much as I like Solingen, and I go there at least once a year, It’s a long ways from Stuttgart. Think of it as an overnight. So I’d pass on that. But if you go, Haribo have their factory outlet there, and the cutlery museum is really good. And Boker knives gives factory tours (although I’m not sure how often in winter.)
And don’t focus on the markets. There are lots of them. Focus on the other stuff. Stay an extra day in Stuttgart and visit the Porsche Museum. (You can rent one of their cars and go for a drive on the Autobahn.) Take a scenic train ride through the Alps. Do some ice skating (they often have rinks at the markets). There’s a lot of stuff to do if you don’t want to stay inside and don’t care about the weather.
Then, it’s not just Christmas day you need to plan for. Things will shut down on the 24th NLT noon. And the 26th is a holiday also. I suggest you find a bigger city, Munich, Zurich, Konstanz, Salzburg for those days, because they will have restaurants and maybe museums open. Or a resort like G-P, because they’re geared for tourists also.
Think about this:
15 -17 Stuttgart
18-21 Konstanz
22-26 Garmisch
27-28 Munich
