The Christmas Adventure at Stockeld Park has lots going on as well as their real ice rink, including their illuminated maze and Enchanted Forest. Areas are priced separately so you can do as much or as little as you like.
The Black Swan at Helmsley have a ‘pop-up’ ice rink just for the weekend from Friday the 2nd of December until Sunday the 4th. Admission is £7.00 per person (30 minutes), and includes skate hire. Festive Christmas drinks of hot chocolate and mulled wine will be available to buy too.
As well as the fabulous ice rink at Yorkshire’s Winter Wonderland in York, there is a large vintage funfair and you can even visit Santa. Beside the rink is PapaKitchen, the new Alpine-themed café a cosy place with rustic wooden tables and benches complete with comforting furs and the warming scent of Glühwein.
Princes Quay Shopping Centre is hosting a Christmas street party for all the family including a Winter Wonderland style ice rink. It seems to be just a one day deal from the information I can find, but is totally free and will run from 11am to 2pm. I have linked to the Hull Daily Mail article above.