Another easy thing to do is use your tractor and a box blade to "pull up" a walking path in your low, wet areas. Build the terrace to follow exactly along a contour line as much as is feasible.
Make a cut on the uphill side with the box blade pushing the dirt to the center line of your path. Then make a cut on the downhill side, also pushing the dirt to the same center line. Go back with your blade level and flatten the top of your path. You can then surface the path with your choice of material - mulch, low growing grass, crushed gravel on landscape fabric, etc.
Your path terrace is also going to CREATE A DAM. In the low spots that are on a slope where the water collects uphill, you will need some version of a pond outlet! It can be a pipe, but frequently it is just a low, cut-out in the terrace to allow water to pass through. In areas where the cut out is sometimes subjected to significant water flows, it needs to be topped with larger rock.
(If you don't own a tractor, I can rent a 32hp tractor and box blade pretty darn cheap in my area. I suspect you can also rent one, and you will go up the learning curve for simple dirt work pretty quickly.)
