  We establish strong uniqueness for a class of degenerate SDEs of weak
H{\"o}rmander type under suitable H{\"o}lder regularity conditions for the
associated drift term. Our approach relies on the Zvonkin transform which
requires to exhibit good smoothing properties of the underlying parabolic PDE
with rough, here H{\"o}lder, drift coefficients and source term. Such
regularizing effects are established through a perturbation technique (forward
parametrix approach) which also heavily relies on appropriate duality
properties on Besov spaces. For the method employed, we exhibit some sharp
thresholds on the H{\"o}lder exponents for the strong uniqueness to hold.
