Updating jailbroken KPW2, also update jailbreak?

[topquark]

I have a KPW2, jailbroken with Niluje's, I think, working fine with screensaver cover hack and all, but I have some issues with the screen fading at the edges sometimes and want to update to the latest firmware . I see that there is a new jailbreak now here that can handle the latest firmware, Winterbreak. But the kindle is already jailbroken. If I do a factory reset and update to 5.12.2.2, do I need to re-apply a jailbreak but this time with Winterbreak? If not, what do I need to do? My main thing I use is only the screensaver cover hack thing.