I dont think a subsoiler is going to help you in the drainage problem. It may allow the surface water to penetrate deeper into the soil but beware that breaking the clay hardpan also will allow you to bog deeper into the ground if you venture into with your tractor. We used them on the farm to loosen up the middle where the tractors tires ran on rowcrop farming. Other than that, they didnt seem to be of much value in increasing root penetration. Most of your usable nutrients are in the top 6 inches of soil for the feeder roots. Tap roots dont seem to have any problem with penetration into tight soils.
A good drainage ditch sounds like what you need to cure your problem. We just finished up with some dozer work laying some rock for erosion prevention, spreading out some dirt piles and while we had the dozer, we had several more ditches opened to remove some standing wet spots from weeping springs. Our land seems to have them at the bottom of every hill. They dont run but just weep and keep large areas wet. We put in some swales to drain them to local creeks nearby to hopefully eliminate the problem. Amazingly the dozer stood up on the mud much better than our tractors which tended to sink deeply into the quagmire. Should have got a photo of my Yanmar setting with the floorboards below ground level a few years ago in one such area. Luckily we had a backhoe nearby to pull me out.