Hi mac_heibu,
There are two different options for using web fonts in Muse: the Edge Web Fonts which are built in to Muse and the fonts from the Typekit library which you can add to Muse via the kit JavaScript.
The Edge Web Fonts are the ones that you see when you choose "Add Web Fonts" in the Muse Type menu:

These font selections are not tied to your Creative Cloud account. Edge Web Fonts is a free service which will continue to work in a site that you built in Muse even if you cancel your Creative Cloud subscription.
You can also use any of the fonts in the Typekit library in a Muse website, as explained in this Muse Insider article: [Edited on 19 March 2018 unfortunately this article is no longer available and the link was compromised.]
These fonts are tied to your account through the Typekit JavaScript you used to add them to Muse. If you choose to cancel your subscription, the fonts will no longer be served to any of the sites which are hosted on your Typekit account. Any site using web fonts from Typekit will display the fallback fonts specified in your font stack or the browser’s defaults.
An alternative is to set up a Typekit account for your client. This allows the Typekit fonts to be one of the deliverables that you hand off to the client when the project is completed. It also attaches the annual Typekit subscription fee to your client's billing information.
I hope that this helps; let me know if you have any other questions! Best,
-- liz