Thanks for the local knowledge Dimlee
I don't have time to do a proper study on this, but I just did a quick Google keyword search for "frozen"+"Rostov"+"November"+"1941" and came up with the following links.
https://warfarehistorynetwork.com/ar...ve-to-the-don/
https://codenames.info/operation/don...ive-operation/
The first link says that they (the Germans) were battling Mud on November 11, and then "A few days later a cold wave arrived and froze everything". This probably doesn't include the Sea of Azov, but a later comment on November 22 speaks of the "now frozen (River) Don".
The second link backs this up with a November 20 reference to fighting on the Don, speaking of "heaps of bodies lying on the frozen river".
So it seems the River Don froze in mid November 1941. I can't see any direct comment on the Sea of Azov, so I can't add anything there.