There are lots of options for automated text messages.

There are lots of settings on the company details page (where you put your company name/number in) under "more" at the bottom, and then select the "texts" tab.

The option for the automated reminders that go out two days before the appointment  is currently only available to be switched off for monthly plans

You can choose what time those texts go out though.

You can also choose if you want texts to go out when you create/copy/move and delete appointments, both to customers and to your employees.

Furthermore, you can turn off texts on a per customer basis and/or a per service basis.