Welcome to the community!
When sending a MMS or picture message it is sent over the network and requires data but you will not be charged any data usage when sending a picture message. So you need to have the data enabled to send and receive the MMS.
If you install the Android messages app and enable the enhanced features you will be able to use the new RCS messaging protocol which is compatible with WiFi but the other person will need to have this also.
You would be able to send and receive messages through WiFi, you can get more info here.