We present Spitzer 3.6 and 4.5{mu}m follow-up of 170 candidate extremely cool brown dwarfs newly discovered via the combination of Wide-field Infrared Survey Explorer (WISE) and NEOWISE imaging at 3-5{mu}m. CatWISE, a joint analysis of archival WISE and NEOWISE data, has improved upon the motion measurements of AllWISE by leveraging a >10x time baseline enhancement, from 0.5yr (AllWISE) to 6.5yr (CatWISE). As a result, CatWISE motion selection has yielded a large sample of previously unrecognized brown dwarf candidates, many of which have archival detections exclusively in the WISE 4.6{mu}m (W2) channel, suggesting that they could be both exceptionally cold and nearby. Where these objects go undetected in WISE W1 (3.4{mu}m), Spitzer can provide critically informative detections at 3.6{mu}m. Of our motion-confirmed discoveries, 17 have a best-fit Spitzer [3.6]-[4.5] color most consistent with spectral type Y. It is likely that CWISEP J144606.62-231717.8 ({mu}~1.3yr^-1^) is the reddest, and therefore potentially coldest, member of our sample with a very uncertain [3.6]-[4.5] color of 3.71+/-0.44mag. We also highlight our highest proper-motion discovery, WISEA J153429.75-104303.3, with {mu}~2.7yr^-1^. Given that the prior list of confirmed and presumed Y dwarfs consists of just 27 objects, the Spitzer follow-up presented in this work has substantially expanded the sample of identified Y dwarfs. Our new discoveries thus represent significant progress toward understanding the bottom of the substellar mass function, investigating the diversity of the Y dwarf population, and selecting optimal brown dwarf targets for James Webb Space Telescope spectroscopy.