Is it free to forward text messages to your Mac?
Text Message Forwarding works via iCloud on your iPhone and Mac. There is no 'extra' message being sent, however this will incur additional data usage if you are not on Wi-Fi.

Text Message Forwarding purely uses an internet connection, whether that be Wi-Fi or cellular data (if enabled). It does not use SMS to forward messages to your desktop. If you don't have an internet connection, the device will wait for network, then send the message to iCloud.