Round dancing on the ice is our 'ice-dancing'. There are some specialities that can be found in the dance circle:

Dancers meet up in the dance circle, like in a ball room. It's the gentleman who asks the lady for a dance or you decide according to the music setting which dance you are going to dance together: ' Do you want to dance the second slow one together?

If you dance in pairs it is possible to combine various dances. Sometimes decorative elements are added and there is always a chance for some creativity.
Some dance partners know each other that well, that you can try out combinations, without leaving the partner insecure (e.g. let go off the hands).
This depends on the individual dancer though - it's the same as on the dance floor, some try out something new and others are happy to dance the basics. Normally it's the gentleman who takes the lead.

A speciality are group dances - the steps are relatively easy - the challenge is the interaction with all the individual dancers. Sometimes it works, sometimes it doesn't.
It's a very special feeling if you do the Killian in a longer chain and all the dancers are pulling in the same direction and the interaction with eachother is working out harmoniously.

It's not common to dance with a fixed dance partner - you take turns. Group dances are also done in various combinations, always depending who is available.