I have examined all Infrared Astronomical Satellite (IRAS) data relevant to the 173 Galactic Wolf-Rayet (W-R) stars in an updated catalog, including the 13 stars newly discovered by Shara and coworkers. Using the W-R coordinates in these lists, I have examined the IRAS Point Source Catalog (PSC), the Faint Source Catalog, and the Faint Source Reject Catalog, and have generated one-dimensional spatial profiles ('ADDSCANs') and two-dimensional full-resolution images ('FRESCOs'). The goal was to assemble the best set of observed IRAS color indices for different W-R types, in particular for known dusty late-type WC Wolf-Rayet (WCL) objects. I have also unsuccessfully sought differences in IRAS colors and absolute magnitudes between single and binary W-R stars. The color indices for the entire ensemble of W-R stars define zones in the IRAS color-color plane. By searching the PSC for otherwise unassociated sources that satisfy these colors, I have identified potential new W-R candidates, perhaps too faint to have been recognized in previous optical searches. I have extracted these candidates' IRAS low-resolution spectrometer (LRS) data and compared the spectra with the highly characteristic LRS shape for known dusty WCL stars. The 13 surviving candidates must now be examined by optical spectroscopy. This work represents a much more rigorous and exhaustive version of the LRS study that identified IRAS 17380 - 3031 (WR98a) as the first new W-R (WC9) star discovered by IRAS. This search should have detected dusty WCL stars to a distance of 7.0 kpc from the Sun, for the absolute value of l greater than 30 deg, and to 2.9 kpc even in the innermost Galaxy. For free-free-dominated W-R stars the corresponding distances are 2.5 and 1.0 kpc, respectively.