This paper reports a Galactic kinematical and dynamical analysis of 1003 main-sequence carbon stars. The sample is drawn from the Sloan Digital Sky Survey, and cross-matched with Gaia DR3 to obtain 6-dimensional positions and velocities using a Bayesian framework. The study provides the first reliable distances for a large sample of dwarf carbon stars, which are then analysed using both space motions and actions. The results are combined with dynamical equilibrium models for the three primary...