Hmm I don't have this problem with my iPad , I'm using iPad 2 with newest iOS . Which iPad do you use?
You can always select this option in your preferences; (Edit) I mean, select to turn off this feature -- I did not feel I was very clear.
You can still link to videos in your signature without showing the actual video player - just use "Edit/Insert Link" instead of "Media". That way people can choose whether to watch or not, and it takes no more space than the text needed to describe the video.
Best part of the whole thread. But OT: I never got the point of pasting the video in the signature. Linking seems better to me.
The gifs I have no issue with if they are small. BUT if it's one like those 3D type ones I've seen where you need 3D glasses to properly see it or it eats your eyeballs or is a small billboard that takes up half the page that's too much.
There is of course "unfriendly" gifs... But a gif still has purpose. Videos rarely would ever fit in the signature dimensions, and signatures are simply just not meant for it... Linking is fine and should be used for videos.