I've read this post and re-read it... and I still can't quite get my mind around it.

There are/were trees, therefore at some point the soil was dry enough, often enough, and deep enough to permit their growth. The trees have died, apparently from drowning.
Does that mean the underground stream is a new event? If so, what has happened to cause the stream to suddenly appear in that locale?

2 feet down is not very far... how big (wide? deep?) is the water... deep enough for you see moving, but is that an inch or a foot of water? Is the water now a permanent feature or is it going to disappear along with the snow? Is it clear? Is it clean? Where is it coming from and where is it going?

I doubt you can answer any of those questions, but I'd suggest checking with a local geologist to at least find out where the stream is coming from and where it is going to. Won't do any good to plant trees if you have a swale in the making. If that 2 foot of soil over the water is soil rather than rock, eventually you may find your self with a surface stream as the covering soil will gradually washes away.

Willows adore being near water (to the extent that they are notorious for invading pipelines) and sycamores are fairly tolerant. But I honestly wouldn't spend the time planting until I knew more about that water.

Cheerful thought: could anyone nearby have put a hole in a water main???

Agree with meldy: what has caused this water to flow now? Clearly trees have been able to establish at some time earlier.

Another serious concern is if your area is prone to severe wind gusts. Trees in sodden ground have a nasty knack of toppling.

Just how far along the 'line' of trees does this underground moving water extend?

People who provide water supplies (utility/municipality) usually have audio equipment that can at least roughly home in on a leak in the line.

If you have your own water tank system - could pay to check for leaks before summer settles in.