I graze most of the wildlife area that I manage. For quail, research has found that bobwhite will almost completely abandon ungrazed grasslands. It is a short time in all but some of the driest areas before the cover gets too thick for bobwhite to use it. They are sight feeders and travel mostly by walking and both of those activities require the more open structure that grazing provides. Also, grazing helps promote/sustain the forb portion of the grassland plant community which are the primary sources for both the insects that the broods require almost exclusively for the first 12 weeks of life and the seed that they consume thereafter.
A wetland system may well perform differently. If it is partially populated by native warm-season grasses (NWSG) there would be little difference with those. If it is more wetland plant dominated, it may be detrimental. The first consideration would be protecting the dam, dike, and water control structures that impound your wetland. Cattle can do severe damage to those structures and they should be protected.
For pheasants, grazing will need to be lighter. The broods will need some of the same structural and forb component conditions as bobwhite, but they may also be able to benefit from higher cover especially in the winter. Care must be taken to provide for that season in the wetland unit if other winter cover is limited!