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Abstract Multiple stable equilibria are intrinsic to many complex dynamical systems, and have been identified in a hierarchy of climate models. Motivated by the idea that the Quaternary glacial–interglacial cycles could have resulted from orbitally forced transitions between multiple stable states mediated by internal feedbacks, this study investigates the existence and mechanisms of multiple equilibria in an idealized, energy-conserving atmosphere–ocean–sea ice general circulation model with a fully coupled carbon cycle. Four stable climates are found for identical insolation and global carbon inventory: an ice-free Warm climate, two intermediate climates (Cold and Waterbelt), and a fully ice-covered Snowball climate. A fifth state, a small ice cap state between Warm and Cold, is found to be barely unstable. Using custom radiative kernels and a thorough sampling of the model’s internal variability, three equilibria are investigated through the state dependence of radiative feedback processes. For fast feedbacks, the systematic decrease in surface albedo feedback from Cold to Warm states is offset by a similar increase in longwave water vapor feedback. At longer time scales, the key role of the carbon cycle is a dramatic lengthening of the adjustment time comparable to orbital forcings near the Warm state. The dynamics of the coupled climate–carbon system are thus not well separated in time from orbital forcings, raising interesting possibilities for nonlinear triggers for large climate changes. Significance Statement How do carbon cycle and other physical processes affect the physical and mathematical properties of the climate system? We use a complex climate model coupled with a carbon cycle to simulate the climate evolution under different initial conditions. Four stable climate states are possible, from the Snowball Earth, in which ice covers the whole planet, to the Warm state, an ice-free world. The carbon cycle drives the global climate change at an extremely slower pace after sea ice retreats. Sea ice and water vapor, on the other hand, constitute the major contributing factors that accelerate faster climate change.