I have never been to Europe at that time of year; it would be too cold for me in central Europe, and I do not like gray weather. However, major cities do not close up shop in the winter. Zagreb in particular has a lot of good museums. The kids will enjoy the Museum of Broken Relationships, the naive art museum is small but very good, and there are many more options. Ljubljana should also be fine in terms of things to do. I'm guessing you'll be OK in Split as well, but I'm doubtful about Kotor. On the other hand, the drive to Kotor will still be beautiful. Dubrovnik? I just don't know.
Plitvice I'd be worried about. You can check the park website (same for the Postojna Caves) to verify off-season opening hours, but the fact is that the walkways at Plitvice are mostly without guardrails. If it's raining or has recently rained, the wood might be slippery. (Snow or ice would be worse.) There are also sections of the paths that are across uneven ground and may be blanketed with dead leaves that are very slippery when wet. The paths are not high above the water, so no ones life would be at risk, but a sprained ankle, broken wrist, or fall into cold water would be extremely unpleasant. I'm not sure what the park will even look like in winter if most or all of the trees have dropped their leaves; I didn't pay attention to how many were deciduous.
Honestly, I also think you've got too many destinations over too many miles for such a short trip. The days will be very short, with far more limited sightseeing hours than in the summer. My first choice at that time of year (weather-wise) would be southern Spain. If the former Yugoslavia is a must even in February, I'd rather combine Ljubljana and Zagreb with Venice or perhaps Graz.
Have you investigated your flight options? They may be somewhat awkward.