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Logic-in-Memory (LIM) architectures offer potential approaches to attaining such throughput goals within area and energy constraints starting with the lowest layers of the hardware stack. In this paper, we develop a Spintronic Logic-in-Memory (S-LIM) XNOR neural network (S-LIM XNN) which can perform binary convolution with reconfigurable in-memory logic without supplementing distinct logic circuits for computation within the memory module itself. Results indicate that the proposed S-LIM XNN designs achieve 1.2-fold energy reduction, 1.26-fold throughput increase, and 1.4-fold accuracy improvement compared to the state-of-the-art binarized convolutional neural network hardware. Design considerations, architectural approaches, and the impact of process variation on the proposed hybrid spin-CMOS design are identified and assessed, including comparisons and recommendations for future directions with respect to LIM approaches for neuromorphic computing.