I have a similar area on my land that's next to a creek. It's impossible to drive anything in that area from winter to the middle of summer. I would have to wait until August to mow that area, and even then, I've managed to get stuck.
After a good mowing, I saw that it wasn't totally flat, and there was an area that was lower then the rest of it that held water longer then the rest of it. I dug a trench to the creek to drain the water and installed three 12 inch plastic culverts. This solved the majority of the problem. It's still wet in the Spring, but now it dries out by May, and I can mow it with the rest of my place.
I dug a test hole with my backhoe in that area in the summer that was about six feet deep. Water started flowing into it pretty quickly. By the time I had a 8x8 foot wide hole dug, the water had filled up that hole to about 2 feet below the surrounding ground. It stayed like that all summer long, butt then collapsed on itself over the winter. I believe my water table is just 2 feet deep in that area.
I might put another pond there, but I haven't done anything since that test hole. My goal is to have more pasture for livestock, so there isn't a need for another pond right now.