Subspace of smooth Foliations inside smooth Distributions - Is it a Frechet submanifold or atleast a Retraction?

Assume M is a closed manifold. Does the set of smooth foliations on M form a Frechet submanifold inside the Frechet manifold consisting of smooth distributions?

If not, can the set of smooth foliations(which is a closed set in the space of smooth distributions) atleast be expressed as a retract of some open set?