You'll need a skin.xml file to pass the required orientation attribute for the menu. In your skin directory, create a new plain text file and rename it to "skin.xml". Into this file, enter the text

<Objects>
  <Object>
    <Token>[SOLPARTMENU]</Token>
    <Settings>
      <Setting>
        <Name>Display</Name>
        <Value>Vertical</Value>
      </Setting>
    </Settings>
    </Token>
  </Object>
</Objects>

If you are using the [NAV] token (instead of the [SOLPARTMENU] token) in your .html skin file, then replace "[SOLPARTMENU]" with "[NAV]" and "<Name>Display</Name>" with "<Name>ControlOrientation</Name>".

Then upload your skin as usual. I didn't test it, because I create my skins directly as .ascx files, but it should work. Good luck!