Openfit Live uses data at rate of about 1.0MB - 1.5MB/minute (60-90 MB/hour) which is similar to streaming music or listening to a podcast.
If you want to save a bit of data during outdoor classes, you can join the class a few minutes before it starts (you'll go into the 'warmup room'), and use your home WiFi to buffer the music. The music will download in the background, and will be ready to play when the class begins.
When the class is about to begin, just switch your WiFi off and head outside!