We investigate the infrared (IR) properties of cool, evolved stars in the Small Magellanic Cloud (SMC), including the red giant branch (RGB) stars and the dust-producing red supergiant (RSG) and asymptotic giant branch (AGB) stars using observations from the Spitzer Space Telescope Legacy program entitled "Surveying the Agents of Galaxy Evolution in the Tidally Stripped, Low Metallicity SMC", or SAGE-SMC. The survey includes, for the first time, full spatial coverage of the SMC bar, wing, and tail regions at IR wavelengths (3.6-160um). We identify evolved stars using a combination of near-IR and mid-IR photometry and point out a new feature in the mid-IR color-magnitude diagram that may be due to particularly dusty O-rich AGB stars. We find that the RSG and AGB stars each contribute ~20% of the global SMC flux (extended + point-source) at 3.6um, which emphasizes the importance of both stellar types to the integrated flux of distant metal-poor galaxies.