The reaction of midlatitude daytime foF2 and thermospheric parameters in two Hemispheres has been analyzed for a minor Arctic Sudden Stratospheric Warming (SSW) in January 2008, three major Arctic SSWs in January 2006, 2009, 2013, and a minor Antarctic SSW in September 2019. Arctic SSWs always result in a simultaneous foF2 depression observed at some stations in the Northern Hemisphere but not necessary in the opposite Hemisphere, that is, not all SSWs have global appearance. Thermospheric parameters retrieved from ionospheric observations in two Hemispheres manifest a dependence on the type of SSW (major/minor) and its magnitude. Pronounced thermospheric SSW effects in the opposite (Southern) Hemisphere may be expected only for strong major Arctic SSW events. Retrieved exospheric temperature does not manifest any visible reaction to SSWs both for major and minor SSW events. The duration of foF2 and atomic oxygen decrease related to SSW is 3–5 days in the vicinity of the SSW peak. Both observed neutral gas density and retrieved thermospheric parameters do not manifest a significant difference comparing western and eastern regions of North America during the minor Antarctic SSW in September 2019. Therefore, the previously reported (80–100%) increase in TEC in the western region of North America was not related with variations of neutral composition and winds.