This paper outlines a methodology for determining the statistics associated with the time evolution of a nonlinear multi-body dynamic system operated under input uncertainty. The focus is on the dynamics of ground vehicle systems in environments characterized by multiple sources of uncertainty: road topography, friction coefficient at the road/tire interface and aerodynamic force loading. Drawing on parametric maximum likelihood estimation, the methodology outlined is general and can be applied to systematically study the impact of sources of uncertainty characterized herein by random processes. The proposed framework is demonstrated through a study that characterizes the uncertainty induced in the loading of the lower control arm of an SUV type vehicle by uncertainty associated with road topography.