Most of the existing self-support topology optimization methods restrict the overhang inclination angle to be larger than the self-support threshold value. However, for some additive manufacturing processes, such as fused deposition modeling, horizontal overhangs with zero inclination angle could be successfully printed while the overhang size plays a key role in determining the printability. Therefore, the self-support threshold condition should be re-developed to comprehensively consider the overhang size and inclination angle. At the same time, there raises the challenges of formulating the self-support constraints based on the new threshold condition. To address this difficulty, a novel method is proposed in this work to realize the design with horizontal overhangs. To be specific, the new method employs a skeleton-based structure decomposition approach to divide the structure into components based on the connectivity condition. Then, each component will be evaluated about its self-support status based on its overhang length and inclination angle. Finally, the self-support constraint will be activated only for those components that violate the threshold condition. An excellent feature of the method is that it can be adapted to address the only inclination angle self-support condition, or the comprehensive self-support condition that simultaneously considers the overhang length and inclination angle. Therefore, the new method serves for general applications to different additive manufacturing (AM) processes. Numerical examples will be studied to demonstrate the effectiveness of the proposed method.