Just want to share what I've just found out...
I have just installed Exchange 2013 and I remember this question: how to add Picture in a signature made in OWA..? While doing some crazy test, I revisited the case and tried one more time to solve this riddle.. Now I finally nailed it!
Assuming you have created your signature (with Picture) using your Outlook Application and had sent emails before;
Now my workaround:
<Copying>
Login to OWA.. Go to your SENT FOLDER. Choose one of your email sent via MS Outlook (with your signature). Copy the signature into clipboard.
<Pasting>
Go to OWA settings, create signature, then paste it (CTRL + V) or whatever.
*** Why not just copy the signature directly from Outlook Application?? Simple, it won't work, believe me, I tried that few years ago. Emails with picture viewed in OWA is "embedded / encoded", so when you paste it, you are pasting HTML code into OWA's signature window.
below is the screenshot.. I thought it's for Exchange 2013 only but tried it in OWA 2010 and it worked like charm.