In short, Yes.
MMS, or picture texts, require data to be sent. Most carriers are deceptive in their advertising around this, often saying you get unlimited text/mms text. Yes, they are unlimited, but only as much as you can fit into your data plan, which includes your internet usage also.
One cool feature of iPhones is iMessaging. If you have an iPhone and are sending a pic or any text message to someone who also has an iphone, and you are connected to wifi, it will go through wifi instead of using your data. For example: You are texting your long distance boyfriend a sexy pic of you from your bathroom. You’re at home and connected to wifi. You have an iphone and so does he. You can send all the sexy pics you want baby, because it really is unlimited, over wifi!
Other options are to just email your pics to your person while connected to wifi. I know this won’t be in the text thread, but it will save your data usage.