In this presentation, we introduce novel structure-preserving methods tailored for the nonlinear Vlasov-Poisson-Fokker-Planck (VPFP) system. By reformulating the VPFP model as a hyperbolic system via a Hermite expansion in velocity space, we develop discretization schemes that incorporate both discontinuous Galerkin and mixed finite element techniques for the coupled equations. We establish exponential relaxation to equilibrium through discrete hypocoercivity arguments, ensuring uniform long-time stability with respect to discretization parameters. Our schemes preserve key physical invariants and maintain the L2 variational structure of the linearized model. Furthermore, we analyze the asymptotic behavior in the quasineutral regime, proving convergence of the electric field to its quasineutral limit with optimal error estimates. Numerical simulations validate the accuracy, stability, and asymptotic preservation of our approach, demonstrating its effectiveness in capturing the long-term dynamics of quasineutral plasmas. This work provides a robust framework for the numerical analysis of kinetic models in plasma physics, with rigorous guarantees in both the long-time and quasineutral regimes.