Most ascents of the Citadel follow routes that exploit weaknesses in the south-facing cliff bands. Most notably, Snoopy's Collar is the narrow chute that splits the east summit from the west. Directly over the intersummit saddle from the top of Snoopy's is a NNE-facing couloir that descends into the very upper reaches of Herman Gulch. The line is deeply inset and narrow at the top and more open at the bottom. On average the slope is moderate at 35-40 degrees however short pockets of steep climbing will be encountered, especially when avoiding runnels that channel rockfall. This chute seems to suck up incredible amounts of snowfall, holding continuous snow until at least the end of June and often into July. Although she refuses to completely reveal herself from below, you don't need to worry about a cornice. The topmost snow, just out of sight from seemingly every vantage point, rolls gently to the saddle.
P.S. I've looked at various Colorado/Front Range guidebooks and have never seen a mention of this route let alone a name for it. If a proper name does exist, I will gladly change it from the bawdy moniker I've temporarily given it.
Start at the Herman Gulch trailhead unless you feel like climbing up Dry Gulch and then passing over the Herman/Dry saddle.
Follow the Herman Gulch trail for approximately 3 miles until the trail starts climbing steeply toward Herman Lake. Leave the trail and begin bushwacking upstream, contouring beneath the headwall that holds Herman Lake. Continue gently upward to the very top of the Gulch beneath the Citadel's imposing NE face. Climb the chute! Initially the snow faces toward the east but turns toward the north as it begins passing through several small cliff bands. The top half becomes more inset and shady, so snow conditions may change substantially as you ascend. Once at the saddle, you can climb either summit via the standard routes. The easiest descent is via the standard route.
Crampons and an ice axe for sure. Because the surrounding cliffs shed a lot of rock, I would strongly recommend putting on a helmet before entering the confines of Snoopy's Backside Chute. ;-)