A lot of the plants that do well in very wet clay can be a bit too vigorous and get a bit too big for most gardens, so I'd be careful with what goes in, but alders, poplars, birches and willows are the typical wetland trees. I think amelanchiers may like the wet as well.
It's maybe worth looking at Salix exigua (the Coyote willow), which is quite a well-behaved willow with long, thin silvery leaves. That'll only get to about 12ft, but it's ok to hack it back anyway to the height you want. It comes into leaf reasonably late, so you can grow spring stuff underneath - like Fritillaria meleagris (the Snakeshead fritillary) and any of the camassias.
The wee shrubby Salix lanata (the Woolly willow) would be good as well, but maybe more as part of a border because that doesn't get any taller than a child.
A lot of primulas and irises are good in those conditions as well. Primulas - alpicola, florindae, all the candelabra types (I like bulleyana, any of the japonicas, pulverulenta and wilsonii var. anisodora). The primulas are well worth starting from seed, so you can have carpets of them. They'll gently seed themselves about as wel. Irises - any of the ensatas or the sibiricas and x robusta 'Gerald Darby'.
Also, I would chance my luck and try growing 'normal' things there - you never know. A lot of things are a lot more resilient than they get credit for, but I maybe wouldn't spend too much on the plants you're gambling on! People have been able to grow apple and pear trees in quite wet conditions.