The easiest approach to Cattail Peak, and the one which I took, is along the Deep Gap Trail (Black Mountain Crest Trail, #179). This trail begins at the picnic area just below the parking lot on the summit of Mount Mitchell in Mount Mitchell State Park.
From the picnic area, take the Deep Gap Trail. At first, the trail is graded and graveled (for the tourists who walk in this far). Within a half mile one reaches the bottom of the gap that separates Mitchell from Mount Craig. Then one encounters a series of extreme ups and downs as the trail negotiates the various high peaks: Craig, Big Tom, Balsam Cone, and then Cattail Peak.
The distance in to Cattail from the Mount Mitchell picnic area is about three miles. Not far, but keep in mind the great swings in elevation as one climbs and descends these major peaks and gaps. There is absolutely no water source of which I am aware along this trail until one gets to Deep Gap (and even then it's a bit of a hike to water).
Good boots. Hiking staff. Take plenty of water.
In winter, be aware that the conditions on the summits of the Black Mountains are as severe as one could imagine. Deep snow is not unusual in the colder months, and instep crampons are advisable in icy weather.
If you have information about this route that doesn't pertain to any of the other sections, please add it here.