My old HTC One V could send and receive MMS picture messages without having to turn on cellular data. So there was never any worry that my small data plan would be exceeded. Not so with my new Moto G and Moto E that require data to be ON. Surprise! Even though data is not actually charged to my plan when MMS are sent there is the likelihood that some other app will use data when it is enabled.
Are there any newer phones that don't need data on to send MMS? I assume it was due to being on the older GSM/CDMA network and the 3G/4G networks require data to be on.
The suggested workarounds for this, ie. use another app like Whatsapp that send data over wifi are at best awkward. You can only send/receive to another Whatsapp user and it doesn't work if you are away from wifi.