Test e-mail with previous version of iOS
The only way to test on a previous version of iOS on an iPad/iPhone/iPod is to actually restore a backup to the version or wipe out the existing version and install a previous version over it.

There's no app that will allow you to do what you're looking for because the devices just won't allow it.

It's rare that an iOS update itself will cause the stock mail app to stop working.  You didn't mention what mail app you were using so I can only assume it's Mail.

With Xcode, you can run various different iOS versions on the simulator only.  If that will work for you then that's your only chance at testing.