As DeBref said, the signature only works for the Mail app. You can add a Yahoo account in Mail by Going to Settings >> Mail, Contacts, Calendars >> Add Account, choose Yahoo and enter your account information. In my opinion this is the easiest way to use Yahoo Mail on the iPad.
From what little I've seen there is no way to set a signature in the mobile version of Yahoo's web browser, and signatures set in the desktop version don't seem to carry over, at least not in the new beta interface.
If you really want to use the web interface, and need the signatures, you could use a third party browser like Atomic Browser and change the browser identity. This will fool Yahoo into thinking you are using a desktop browser, and you'll get the full desktop version. You'll need to spring for the full version of Atomic Browser to get the ability to change the browser identification. There are other browsers that can do this, but Atomic is the one I'm most familiar with.
Not everything may work as expected this way. I did a quick test of the new beta interface. It warns that the iPad does not have the the screen resolution recommended, and that it may not work right. Indeed, it is a little quirky in landscape mode, but seemed to work well enough in portrait. I did not do a full test of the site, so you are on your own.