Cool subdwarfs of types K and M are the fainter counterparts of cool main-sequence dwarfs that dominate the Galactic population. In this paper, we present the results of an optical speckle survey of 62 confirmed cool subdwarf systems within 60 pc. We have resolved two new companions and confirmed two previously known companions with separations 0. 13-3. 29. After including previously known wide companions and all known spectroscopic binaries, we determine the multiplicity rate of cool subdwarfs to be 26% ± 6%, which is somewhat lower than comparable main-sequence stars that have a multiplicity rate of 37% ± 5%. We find that only 3% of the cool subdwarfs surveyed have companions within 10 AU, 3% have companions between 10 and 100 AU, and 14% have companions beyond 100 AU. The other 6% of cool subdwarfs are spectroscopic binaries. This is very different from K/M dwarfs that have most companions (13%) at separations closer than 10 AU. However, because a search for close binaries among a large sample of nearby cool subdwarfs remains elusive, it is not yet settled whether or not the multiplicity rates are significantly different. Nonetheless, several different observational results and theories pointing to a possible dearth of subdwarf multiples are discussed.