To achieve the goal of high wind power penetration in future smart grids, economic energy management accounting for the stochastic nature of wind power is of paramount importance. Multi-period economic dispatch and demand-side management for power systems with multiple wind farms is considered in this paper. To address the challenge of intrinsically stochastic availability of the non-dispatchable wind power, a chance-constrained optimization problem is formulated to limit the risk of supply-demand imbalance based on the loss-of-Ioad probability (LOLP). Since the spatio-temporal joint distribution of the wind power generation is intractable, a novel scenario approximation technique using Monte Carlo sampling is pursued. Enticingly, the problem structure is leveraged to obtain a sample-size-free problem formulation, thus making it possible to accommodate a very small LOLP requirement even with a long scheduling time horizon. Finally, to capture the temporal and spatial correlation among power outputs of multiple wind farms, an autoregressive model is introduced to generate the required samples based on wind speed distribution models as well as the wind-speed-to-power-output mappings. Numerical results are provided to corroborate the effectiveness of the novel approach.