Modern browsers use secure cookie files, and there is nothing to be afraid of in their storage.
Except for linking all your visits to a certain website, which is bad for privacy.
In the standard build of the TOR browser
The default of Tor browser is a lot better: it doesn't store cookies:
Cookies are only valid for a single session (until Tor Browser is exited or a New Identity is requested).
it is not possible to transfer information about cookie files from one site to another.
The privacy risk involves more than just "other sites": it includes not telling just one site that you've visited it before.
In short: cookies are bad for privacy, no matter what's in there.