Strollers allowed at your ice rink?

I just came from looking at a pic of Heidi Klum ice skating, pushing her daughter in a stroller. Is this allowed at most rinks?

Interesting question! I have never seen such a thing. I have seen those pushing things like "walkers" in the past, but not anything like a stroller. I wonder about those things babies sit in and scoot around using their feet (not sure what they are called)... seems more reasonable than a stroller, maybe something adapted to ice.