Can trees help with drainage?

Can trees help to suck up water from very wet pasture? We have dairy cows, and next year we want to divide the field into for example 14 different paddocks (so each can rest two weeks if they are grazed for one day). If this works out we can make them permanent, and make the divisions with trees (maybe hedgerows). I am wondering if it is possible to achieve many things at once: better pasture (rotational grazing), forage and fodder from the fence trees, and then maybe also some help with evaporating some of the water through the action of the trees. It is espoecially this last point I would like some opinions on. It is wet all year here. Possible frost from November till March. I know a growing tree drinks a lot of water in a day, but what about a tree in winter? We have only a shallow layer of soil on top of the bedrock. Orientation north and north-west, mostly sloping. Mild coastal climate, south western coast of Norway, northern Europe, altitude of Scotland. Thank you for all input.

A type of evergreen tree like a pine would use water most of the year because they don't drop their leaves and their sap doesn't freeze. Deciduous trees on the other hand, drop their leaves in the Fall and go dormant during the winter. They don't start using water again until the spring when they grow new leaves.

Pine needles, however, would not make good forage for livestock.

Transpiration is a function of humidity, circulation and temperature... there is no pumping, rather moisture is drawn from the tree by the atmosphere. So under cool humid conditions transpiration would also be slower than during warm dry conditions. Like John said -- no leaves, no transpiration.

I would also consider the landscape position and soil conditions. If the soil is wet because it is compacted, that is different than if it is wet because it is at the bottom of a hill. It could be that your rotational grazing will increase root activity by pasture plants, increase worm activity, and reduce hoof compaction, making your site less wet, IF soil porosity is what is making your soil wet.