The terms of service states that “you grant Snapchat a worldwide, perpetual, royalty-free, sublicensable, and transferable license to host, store, use, display, reproduce, modify, adapt, edit, publish, create derivative works from, publicly perform, broadcast, distribute, syndicate, promote, exhibit and publicly display that content in any form and in any and all media or distribution methods (now known or later developed).”
Basically, they can do whatever they want with everything. However, this is nothing new. There is a similar paragraph in the previous version of the terms of service on WayBackMachine stored in July.
Snapchat specifically wants to clarify in its blogpost that messages are not stored permanently after they have expired or been viewed. The post reads, “Snapchat is not – and never has been – stockpiling your private Snaps or chats, and because we continue to delete them from our servers as soon as they’re read, we could not – and do not – share them with advertisers or business partners.”