I have an area like you seem to have, and about the same acreage in size as well, used by both wildlife and my grazing sheep alike. Last year I installed swales in the area with great success.
Swales:
For my swales it took the run off from two culverts draining a steep (9% grade) 25 acre field and contained the water flow. Immediately upon getting to the last culvert my straight swale went to some meandering paths that followed contour and checked with rock dams to prevent erosion. Overall this works well at draining and containing my excess water.
Grazing:
Here is the skinny on grazing wetland. It can actually work to a farmers benefit, but here is the problem. Wetland grass matures REALLY fast, about the same time as dandelion or orchard grass. Unfortunately most grazing livestock do not like wet feet if they can help it, so the sward reaches maturity before the livestock get to an area they really want to graze. Now unpalatable, the animals do not graze it leading the farmer to conclude that livestock dislike wetland grass, when that is not true at all. This same holds true for
hay and forage as equipment cannot get on the wet area in time to harvest the sward when it is palatable. In short, livestock love wetland grasses, it just has to be really early in the growing season!
I am able to counter this problem a little by bush hogging the thick grass when it is dry
enough to get on it. That gets the second crop growing and my sheep, now happy to graze with dry hooves, get on it merrily. In fact right now this area is really nice because we are in a drought and this area is acting as a sort of "grass reserve", sadly though it is only an acre in size. Still it is better than nothing.
As my Agronomist has always told me, "Fail Small", so in trying to work this area into something usable, to actually find a prescription that works is kind of nice, and now I can replicate what I have done on this acre, to other wet areas that need refining as well. (Maybe anyway, see laws below).
Laws:
Sadly I was only able to do this because the required "Wetland Determination" for some reason did not determine this area was a wet area. Had it been identified, I would have been in conflict against the "Swamp Busters Act", as well as against environmental law for state, federal and now Army Corp of Engineer laws. So the question is, do I do what I know is right for my farm and sheep, or get the required wetland determination which will limit what I can do inevitable in some locations of my farm? I do not have
the answer for the latter, and bring this up only so that you (and others) know farming wetland right now is quasi-legal.