I wonder what the rinks would make of a skateboard with ice blades...
Probably wouldn't allow them, due to them not being attached to the skater, and being a potential trip hazard; then again they allow penguin/seal skating aids on the ice.
You could try wearing curling shoes (for grip) to help propel you along too.
Possibly setup their own session, similar to 'stick and puck' sessions, so you could have jumps and cones on the ice.
For some reason I thought of the Doncaster Dome, "
the UK's only split-level Ice Rink" <- probably be a good place to have a play.