Can I send mass outbound SMS messages to my customers?
It is not possible to natively send mass outbound SMS messages with the default Text functionality. There are carrier restrictions on the long code numbers offered in Zendesk Talk so we do not recommend trying to achieve this.
We have some partners that can help in this regard though, and because that functionality is something they solve for, you wouldn't run the risk of hitting a carrier limitation.
Use Google to search for Mass outbound marketing SMS Zendesk to yield some partners that offer this functionality. Twilio is one such partner that provides this functionality, and they have an integration with Zendesk.
For more information on sending and receiving texts with Zendesk, see this article: Getting started with Text.