I'm not going to let my daughter go ice skating
Why won't you let your daughter go ice skating?
It's too dangerous for children.
I can see your point, and I understand it. Sometimes kids need to hear no, if doing something could be dangerous for them. I think you just need to explain to them why you are saying that.
I'm her father and I don't have to explain all of my actions to her. What I say goes.
It's okay to stop your children from an activity that could lead to injury, but you should explain why so they understand. Without understanding why, she may resent you for keeping her away from fun activities.