This paper suggests and explores mechanisms relevant to millennial-scale climate variability during glacial periods. In particular, we present the results of model studies that are able to reproduce many aspects of observed glacial climate variability (e.g., Dansgaard-Oeschger oscillations) without external forcing and that provide a natural explanation for the prevalence of high-amplitude variability in glacial climates and the relative stability of the Holocene. We show that the role of sea ice is critical to cold climate variability because of the effective reduction in the high-latitude meridional sea surface temperature gradient resulting from sea ice expansion and the associated role of sea ice in inhibiting heat flux from the ocean to atmosphere. Thus as sea ice expands in a cooler climate, the high-latitude oceanic heat loss to the atmosphere is inhibited, the thermohaline circulation weakens, and the sinking regions move equatorward, leading to a shallower and weaker deep circulation. This weak circulation is unstable, and intermittent high-amplitude oscillations occur on a timescale and with a spatial structure very similar to Dansgaard-Oeschger cycles. Consistent results are found using both a three-dimensional ocean circulation model coupled to an energy balance atmospheric model and with a much simpler ocean box model. In general, freshening plays a secondary role in the weakening of the North Atlantic thermohaline circulation. Significant freshening is required to alter the stable northern deepwater formation that occurs in a warm climate such as today's Holocene, but once this freshening threshold is achieved, the thermohaline circulation shifts to reverse overturning with sinking in the tropics.