The effects of Space Weather events on cosmic rays detected by the Solar Neutron Telescope (SNT) at Sierra Negra, Mexico, were studied. The SNT is part of the Sierra Negra Cosmic Ray Observatory (SN-CRO), located at 4580 m a.s.l. We analyzed the data recorded by six SNT channels (C2, C3, C4, N2, N3, and N4) during geomagnetic storms from December 2015 to December 2022. Using the Dst and Kp indices, 30 moderate (Dst < -50 nT, Kp ≥ 5) and intense (Dst < -100 nT, Kp ≥ 7) geomagnetic storms were selected. The C2, C3, C4, N2, N3 and N4 channels detect charged and neutral particles, respectively, with energy deposition thresholds of E > 60, 90 and 120 MeV. The counting rates of these channels present diurnal variation, which was removed with the seasonal trend decomposition using Loess method. After data treatment, either significant decreases or enhancements were observed in the trend of at least one SNT channel for 21 of the analyzed events. Two confirmed Forbush decreases were also identified.