I had not tried to send a video yet, so after seeing this I tried it. I saw that there was no choice to pick messaging when you try to do it right from the video. Then went and started a message and hit the attachment button and chose video. (Yep, video was a choice!) The video I picked was a very short one of my dog and sure enough, it said, "You can't add this video to your message."
I wonder why this is and hope it is something fixed with a future update maybe. First thing I've seen that disappoints me with my Ultra. Drat!
(Thought I'd add that I am referring to sending a video by SMS, not email, since that wasn't clear in the first sentence. I have sent a video by email.)