Set your automatic out of office reply under the Outside My Organization tab. This is for people outside your company such as clients and suppliers. You can copy what you typed in for Inside My Organization or you can put something else for people outside your organization. You can even untick the “Auto-reply…” box if you don’t want to send them an automatic reply while you’re away.
A thing my employer does is when someone leaves, they just shutoff the email. So someone goes to the trouble of writing an out of office explaining that they have retired or accepted a job somewhere else and where someone can go for help and IT just nukes the email address 24 hours after the person leaves. Then whomever was contacting them has no idea where to turn next. It is a terrible policy.

While not QUITE as annoying as “Have a great day!” there are several people/departments who use an auto reply for the most frequently asked questions or information for their department…something along the line of an IT auto response that says: “To submit an IT request or check for an updated status on a request, please visit request.business.com”
There's a term that we like to use around here called "snowbirds," which is used to describe those who once resided in the northern part of the U.S., only to flee to warmer parts of the country during the winter.