Is texting free when you have Wi-Fi?

I have an iPhone and I'm over Wi-Fi and texting someone. Does it count on my my number of text? And btw I have Verizon

No- it still goes on your texting plan. Wi-Fi is just for internet unless you have another text program you use instead.

Textings done on your cell plan, Wi-Fi only covers internet on your phone

Yes it will. I'm sorry. It is NOT free. There's no such thing as a "free lunch" in life.