Cookies are not saved in private windows but there are such things as "browser fingerprinting" which can still identify you uniquely, by looking at things like your screen size, which extensions you have installed, and so on. Privacy modes are getting better at dealing with these things, but so are advertisers.

If you want to protect your privacy even better than with a private window, you can look at setting up a second Firefox profile. If you install different extensions in the other profile and only use websites in one profile or the other (never both) then it will be much more difficult to tie both profiles together as belonging to the same person.