No, it's part of your service with your carrier. But they limit you.
I'm with T-Mobile and the current plans limit data roaming to 200mb. I'm on an older plan so my data roaming limit is probably less. But after 200mb on the current plans T-Mobile will stop you from using data when roaming on another network.
This is per month.
Some carriers used to charge extra, some still might. This is why the option to prevent Data Roaming on the phone still exists. If you turn it off, the phone will not use data when roaming - and you don't get charged.