Changing default font type on all emails the system sends

Your markup looks correct. What email client are you testing this on? Not all email clients support the use of web fonts. I don’t think Gmail supports web fonts.

Try adding a div with the class you are wanting to style directly to the invite template and then adding styles to the class to the Email Style / CSS editor. Discourse will substitute the styles you add there directly into the div that you target with a class. For example, with the Invite Mailer template customized to:

<div class="invite">
%{inviter_name} invited you to a discussion

> **%{topic_title}**
>
> %{topic_excerpt}

at

> %{site_title} -- %{site_description}

If you're interested, click the link below:

%{invite_link}
</div>

and the following added to Email Styles / CSS

.invite {
    border: 1px solid red;
}

Invites have a red border around the content.