We do it all the time. Like a previous poster said, you can't bring them to AK but the other parks are all fine.
Our DS is now 4.5 and has been obsessed with those Mickey head balloons since his first trip at 18 months. We get him one on every trip (it's one of the first things he insists on doing) and then we have to drag that damn thing around for the rest of the trip. Like I said, he loves them so we'll continue to get him one, I am sure, but we constantly curse the bloody thing when it's tied to the stroller we are pushing and it's hitting us in the head (as we hold it so it doesn't hit other guests in the head). Sorry for the tangent - we have a love/hate relationship with the balloons!!