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, we went around the area in January and had a lovely time.
In regards to Hainach, we had an unexpectedly magical visit there, though this was entirely due to the circumstances of our visit and the unique snowfall we encountered. March may start to show the start of spring colours, but probably may be a little underwhelming.
Unless you have your own transport it may prove difficult to get to the WHS inscribed core of the site. The more accessible tree top walk isn't actually in the WHS, you may be able to hike into the core zone from there though. Unless you have a particular desire to see it then it would probably be one I would skip (I won't judge you if you go there, we did and that is the joy of this hobby). If you are there, then you will be close to Eisenach where Wartburg Castle is.
I liked Erfurt, impressively situated cathedral and the bridge is nice, plus it is in the area of the tentative World Heritage site
, which is pretty underwhelming, but perhaps worth a visit. On the bridge is a magnificent Chocolate shop and Ice Cream parlour
, which I wouldn't skip.
In regards to the Erzgebirge, we had a nice time driving around. Freiburg was my favourite place up there. But that is perhaps more because I am interested in urban sites than industrial aspects. There were some nice looking museums explaining the industrial aspects, but they were all closed when we visited (right after New Year). If you do end up there I will give a hat tip to Stadtwirtschaft
a wonderful half Czech half German pub.
Annaberg-Buchholz didn't grab me as much but we only had a quick and very cold visit. We also visited Seiffen, which was very touristy, but fulfilled our Christmas decoration requirements perfectly.
That weather seems about right (had to run it through a converter as my Fahrenheit knowledge is pretty patchy.)
Don't skimp on time in Dresden either, it may not be a WHS any more, but it is one of Central Europe's finest cities and the museums are excellent.