Network control strategies for energy-efficient operation of HetNets need to match the dynamics of spatial and temporal traffic loads and to stabilize the network. In this paper, we develop a stochastic optimization framework, which formulates spatially inhomogeneous traffic distributions and time-varyingly random traffic arrivals and guarantees network stability, to investigate the energy conservation problem in HetNets. In particular, we jointly optimize base station (BS) operation, user association, subcarrier assignment, and power allocation to minimize the average energy consumption. We devise an algorithm without requiring any prior-knowledge of traffic distributions, referred to as the Steerable Energy ExpenDiture algorithm (SEED), to solve the problem. To deal with a highly coupled and mixed combinational subproblem in the SEED, we separate optimization variables for suboptimal but cost-efficient and easy-to-implement algorithm design. By this, we develop closed-form solutions for both user association and subcarrier assignment, a fast and tuning-free algorithm that provably achieves at least local optimality for power allocation, and a greedy-style heuristic algorithm for BS operation with polynomial complexity. Simulation results exhibit that the SEED usually converges fast, can flexibly tune the power-delay tradeoff, and can significantly reduce energy consumption against other existing schemes.