In this article, we propose a distributed demand-side management (DSM) approach for smart grids taking into account uncertainty in wind power forecasting. The smart grid model comprehends traditional users as well as active users (prosumers). Through a rolling-horizon approach, prosumers participate in a DSM program, aiming at minimizing their cost in the presence of uncertain wind power generation by a game theory approach. We assume that each user selfishly formulates its grid optimization problem as a noncooperative game. The core challenge in this article is defining an approach to cope with the uncertainty in wind power availability. We tackle this issue from two different sides: by employing the expected value to define a deterministic counterpart for the problem and by adopting a stochastic approximated framework. In the latter case, we employ the sample average approximation (SAA) technique, whose results are based on a probability density function (PDF) for the wind speed forecasts. We improve the PDF by using historical wind speed data, and by employing a control index that takes into account the weather condition stability. Numerical simulations on a real data set show that the proposed stochastic strategy generates lower individual costs compared to the standard expected value approach.