Did you try long pressing the image to get a dialog box with options including to save to the phone?
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.
Connect to Wi-Fi, that will most likely be the only way you will be able to download without using your data. Otherwise, if the image is showing in your MMS then it has already been downloaded and has used your data. There should be a setting within text messages or possibly within the mobile networks to either enable or disable auto-downloading of messages/pictures.