Sometime back, Mozilla has made available preview of Firefox for Windows 8 in Aurora channel, the latest development for that is they’ve started implementing Private browsing and added basic support for it to Nightly version, right now PB is disabled by default, you can enable it by toggling a preference in about:config.
How to enable Private Browsing for Metro Firefox in Windows 8
1. Make sure you’ve installed latest Firefox Nightly and set it as default browser.
2. Reach Start Screen and click on Nightly tile to enter Windows 8 Touch mode, type about:config in the address bar at the bottom and press enter
3. Find metro.private_browsing.enabled preference and toggle its value from (default) false to to true.
After enabling it, when you click on navbar menu icon, you can see ‘New Private Tab’ option above ‘Relaunch in desktop’.
"Private tabs are displayed in the tab strip like regular tabs, but with a solid purple background in place of a thumbnail".
Happy Private Browsing testing of Firefox in Windows 8..