So three ideas come to mind:
1) Gradient.
Is the land flat or nearly flat? Could it be gently reshaped to allow a few catchment areas? Think of it like wet weather ponds that slowly let the water seep in, but leave the rest of the area dry enough to work with.
2) Trees and pasture can work well together. Plant some thirsty trees to help draw up the water and to provide some shade. This will have the impact of putting down roots that will help get the water down to the subsoil layer too.
List of Standing Water and Wet Soil Trees All of the trees listed below will flourish in wet areas, even standing water: Atlantic White Cedar Bald Cypress Black Ash Freeman Maple Green Ash Nuttal Oak Pear Pin Oak Plane Tree Pond Cypress Pumpkin Ash Red Maple River Birch Swamp Cottonwood Swamp Tupelo Sweetbay Magnolia Water Tupelo Willow
https://www.gardeningknowhow.com/ornamental/trees/tgen/wet-soil-trees.htm
3) Do a soil test and see if you have enough organic matter in your soil. If you have compacted clay, it would have trouble draining. Additives can help you nudget it n the right direction. Wood chips,
Compost tea, or even lime/ash dust could help speed up the transformation. There are some great soil building threads here on permies and a resident guru RedHawk.