Normals with unknown variance (NUV) and, more generally, normals with unknown parameters (NUP) can represent many useful priors including L_p norms and other sparsifying priors, and they blend well with linear-Gaussian models and Gaussian message passing algorithms. In this paper, we elaborate on recently proposed NUP representations of half-space constraints, box constraints, and finite-level constraints. We then demonstrate the use of such NUP representations for exemplary applications in model predictive control with a variety of constraints on the input, the output, or the internal state of the controlled system. In such applications, the computations boil down to iterations of Kalman-type forward-backward recursions, with a complexity (per iteration) that is linear in the planning horizon. In consequence, this approach can handle long planning horizons, which distinguishes it from the prior art. For nonconvex constraints, this approach has no claim to optimality, but it is empirically very effective.