This article investigates the privacy-preserving distributed online stochastic optimization problem with random parameters following time-varying distributions, where a set of nodes cooperatively minimize a sum of expectation-valued local cost functions subject to coupled constraints. First, a function-decomposition-based privacy-preserving method is provided to preserve the private subgradient information of each node, which can guarantee both privacy preservation and convergence accuracy. Then, a privacy-preserving distributed online stochastic optimization algorithm is proposed based on the primal-dual method. It is proved that the dynamic regret and the constraint violation are sublinear. The relationship of the dynamic regret between before and after function decomposition is provided, and so is the constraint violation. Finally, a numerical simulation is provided to demonstrate the effectiveness of the proposed algorithm.