If you add custom HTML to your site this will not display on the mobile version of your site by default. This is to prevent your site from breaking should you use a code snippet that is supported by desktop devices but not mobile devices.
However, you can choose whether you wish it to display or not. When you add code to an HTML widget you will see a radio button that says Display in Mobile. Check this button if you wish your custom HTML to display on the mobile version of your site.
If you enable a code snippet for mobile, be sure to check your mobile site to be sure that it works and does not cause any unintended issues with the rest of your site. If it does you have the option to disable it again by unchecking the button.