You can forward any images sent to you in the Messages app by simply pressing down on the image bubble until the "Copy/Save/More..." button pops up on your display. Tap the "More..." option, then select the image you want to forward and tap the arrow icon at the bottom of your display. This will open a new message window where you can type the phone number or name of the contact you want to forward the image to.
iPhone 6s and 6s Plus owners can also use 3D Touch to copy, save or forward an image. Just use a hard press to pop open the image you want to forward, then swipe up to open the Copy/Save/Forward options.