Open quantum systems and their dynamics are usually studied in terms of reduced density matrices, i.e. by a non symmetric description which is very useful whenever one of the two subsystems is to be considered an environment. However, the loss of information implied by the partial trace over the environmental degrees of freedom can have severe consequences. In this work we consider the dynamical evolution of a composite system in terms of the parametric representation with environmental coherent states, which is still non symmetric but yet exact. General features of the approach, as well as some specific results for a paradigmatic model of decoherence, are presented; the effects of the environmental quantum-to-classical crossover on the dynamics of the principal system are finally discussed.