If weakly interacting massive particles (WIMP's) are the dark matter in the galactic halo, they may be detected in low-background ionization detectors now operating or with low-temperature devices under development. In detecting WIMP's of low mass or WIMP's with spin-dependent nuclear interactions (e.g., photinos), a principal technical difficulty appears to be achieving very low thresholds (<~ keV) in large (~ kg) detectors with low background noise. We present an analytic treatment of WIMP detection and show that the seasonal modulation of the signal can be used to detect WIMP's even at low-signal-to-background levels and thus without the necessity of going to very-low-energy thresholds. As a result, the prospects for detecting a variety of cold-dark-matter candidates may be closer at hand than previously thought. We discuss in detail the detector characteristics required for a number of WIMP candidates, and carefully work out expected event rates for several present and proposed detectors.