In this talk, I will introduce restricted Poisson algebras in characteristic two and explore their connection with restricted Lie-Rinehart algebras. For the latter, a cohomology theory is developed and abelian extensions are investigated. I will also construct a cohomology complex for restricted Poisson algebras in characteristic two that controls formal deformations. This complex is shown to be isomorphic to the cohomology complex of a suitable restricted Lie-Rinehart algebra. Several examples are provided to illustrate the constructions. This is joint work with Sofiane Bouarroudj and Quentin Ehret.