Your answer is that the use of an iframe in an email message is not well supported.
See
this[
^] as a reference.
This is also not the correct way to embed a youtube video in email. If you go to youtube and share a video via email with yourself you can inspect the html content of that email to discover how you should embed the video properly.
A static-clickable image that will redirect the user back to youtube.
<a href="http://www.youtube.com/watch?v=Bk_6r-b3kqU&feature=em-share_video_user">
style="text-decoration:none;display:block"
class="nonplayable"
target="_blank">
<img src="http://i3.ytimg.com/vi/Bk_6r-b3kqU/mqdefault.jpg" height="274" width="498">
</img></a>
A playable video(requires flash player)
<embed width="640" height="385" base="https://www.youtube.com/v/" wmode="opaque" id="swfContainer0" type="application/x-shockwave-flash" src="https://www.youtube.com/v/Bk_6r-b3kqU?border=0&autoplay=1&client=ytapi-google-gmail&version=3&start=0">
</embed>