I have heard that it is possible to browse with the Tor browser without getting cookies. When I take a closer look it seems like it is excepting cookies.
You're messing two different things up:
- Tor - an anonymous network of darknet type to keep it's users private. It does not gives a thing about anything protocol-related, including HTTP and including Cookies
- Tor Browser - a fork of Firefox focused on privacy. It is designed to work with Tor network, but actually it works with any TCP/IP connection based network, including clearnet
To avoid cookie-tracks use Firefox addons, the Tor network itself has nothing to do with them