I have had a Galaxy S2 for 2 years. I just upgraded to the S4 3 weeks ago.
Until this morning, I was able to send SMS messages without data mobile being on via my Wi-Fi connection. I have made no alterations to my phone other than trying out various suggestions on given on forum sites. I have tried 3-word messages as a test and even these are converted to MMS.
I have loaded both Handcent and Bigsms. They work, but why should I have to have these after 2 years and 3 weeks without a problem?