I guess you have to define "cohesion". From the Mohr envelope perspective (along with general practice) the tests on cohesive soils are performed in a saturated condition - so there is no issue of the moisture content. Cohesion is the intercept of the failure envelope when the average deviator stress is zero.
Now if you are really talking about undrained shear strength at varying moisture contents - yes the shear strength can vary with moisture content. Take a mud soup and let it dry and the shear strength will be greater. Rewet it and the strength will lessen. This is not "cohesion" this is undrained shear strength, which can vary with moisture content.
One of the big problems with subgrade failure is when rutted sites become dry and the subgrade "passes" a proofroll. With an ensuing pavement job, there may (will likely) be premature failure as the subgrade rewets and the traffic loads begin.
Now, if you properly compact a subgrade (i.e., start with some engineered strength at a favorble moisture content), there may be some increased dry strength, but upon rewetting, the original strength will remain intact. Similarly, if you properly compact a fill and it becomes saturated, it will unlikely go to mush.
Just one man's opinion.
f-d
¡papá gordo ain’t no madre flaca!