We had an awesome day sledging at Ártúnsbrekka Ski Slope. The lift was closed when we came (due to covid) but when it is running it´s FREE. Ártúnsbrekka is one of three slopes with a ski lift in Reykjavík. The other two being Seljahverfi and Grafarvogur. All three of these city slopes (and lifts) are FREE to use.
Skiing and snowboarding is popular with families in Reykjavík. I´d say Seljahverfi is probably the most gentle incline out of the three city slopes but all three are designed for kids / beginners so they are all perfect places for kids to learn!
You can check this facebook page for opening times.
For info on larger slopes and ski passes click here