Yes, we've been every year with our 2 fir the last 4/5 years. It's lovely and christmassy and feels like the official start of our festive season. Not sure what the package we do is as we go with orhers who book it it but we usually do about an hour at 6pm.
Been to Somerset House in the past but always found it very crowded and impossible to find a seat in the cafe which is not accessible during the session. We go to Hampton Court palace now. Much less crowded and lovely setting. Nice spacious cafe with lots of seats and can access it during the session if you need a quick break.
I went quite a few years ago, just to skate, and it was lovely. There are many places to eat and drink on the Strand so I'd probably just book the skating then head off somewhere else as Somerset House can get pretty overcrowded.