What you need to do is think of a way to drain the tree line area. When the ground is frozen the water cannot sink in and it will go to the lowest point and sit if there is not a way for it to flow to a stream or river.

It could be that human activity in the area (such as road building) cut off the path of the water where it used to flow, so now it just sits.

Typically the solution is not cheap, you need to find a way to drain the water and that generally means putting in underground pipe to tunnel under whatever is keeping the water in place until it gets to a place where it can drain into a river or other lower elevation.

When this happens in a city with storm sewers typically a drain is put in the lowest part of the backyard (or frontyard, as the case may be) and underground pipe (black plastic stuff) is run out to the street where the water will then flow out and into a storm drain.

I'm guessing you live in the country without a storm drain nearby so you'd need to pipe to a river or stream or something. You're probably looking at several thousand dollars, but maybe the corn field owner would split it with you.