There are many willows smaller than the Weeping willow. Pussy willows of many types and colors as well as some others. Chokeberry bushes can live in these conditions as well. Button bushes like wet areas and some of the Cedars will thrive there. Nishiki willows, both ground and on a standard do well in wet conditions. Look at wet list plants for your area and you will get many ideas. Some others are the Arctic willow and Corkscrew willow. Laurel Leaf willows are stunning and look muck like an outdoor Ficus tree. They will get quite large, however.

Nothing will 'use up' water in the way you want - wet soil will stay wet, whatever you plant. But some trees like wet soil, so they are the ones to grow.

The best two are Baldcypress and Dawn Redwood - fast growing, large, long-lived. Willows also do well, but are typically short-lived and prone to various diseases; they can be good for attracting wildlifr though. "some of the Cedars will thrive there" - not true! Cedars need good drainage, and wouldn't do well. Other good trees for wet soil include Swamp White Oak, Sweetgum, and Tupelo.

Resin

partial list:

Around the fringe of a swamp, zone 7-8
Coast Redwoods
Sequoias
Western Red Cedars of many varieties (but they don't like standing water for long)
Shore Pine (Pinus contorta var contorta)
Leylands
Blue Atlas Cedars
Gingkos
Red Horsechestnuts
Purple Robed Locust (Robinia 'Purple Robe')
Giant Dogwood (Cornus controversa)
Quaking Aspen
Catalpa
Sugar Maple
Raywood Ash
Green Ash
Nellie R Stevens Hollies
Himalayan White Birch
Japanese Maples
Quercus virginiana
Quercus myrsinifolia

In the swamp: (6-11" pooling water in winter)
WILLOWS -- Prairie Cascade Willow -- awesome, truly amazing tree
Babylonica Weeping Willow
Curly Willows
Blue Arctic Willows
Rosemary Willows
Nishiki Dappled Willows
Red Barked Willow (Salix alba 'Chermesina')
Violet Willow (Salix daphnoides)
Lapland Willow (Salix lapponum)
Bay Laurel Willow (Salix pentandra)
Swamp Tupelo (Nyssa aquatica)
American Sycamore Buttonwood (Platanus acerifolia 'Bloodgood')
London Plane Tree (Platanus occidentalis)
Sweetgum
Black Cottonwood
Bald Cypress
Blueberries
2 kinds of swamp Eucalyptus
Swamp White Oak
Swamp Red Maple
Swamp Magnolia

Double check the mature heights of these suggestions, if you really don't want a large tree - some can get quite large - both tall and wide. Others will stay reassonably small.

I can see not wanting a lot of tall trees on 2 acres, and I don't know what you already have, so I may be out of line, but one or 2 largish ones in the low area might be nice. I do think that having a range of heights in a planting is better looking than an even row - or a mostly even row.

There are also a lot of shrubs that will do well in wet soil. I am not sure what will grow in your area, but around here there are, among others:
Itea virginana
Zenobia pulverulenta, Dusty zenobia
Arborvitae in various cultivars
Chokecherry
Lindera benzoin, spicebush
deciduous hollies, various (remember you will need one male to every 5-7 female plants to get berrries)
Clethra alnifolia
Calycanthus floridus

Any of these that will grow for you offer either flowers or berries or good autumn foliage color, sometimes together. Some will sucker, and make good-size thickets, so look at that too. It's usually easy to pull or dig the suckers in the spring, if you want to. Either toss, replant elsewhere or pot up to give away. Sometimes nurseries, if a plant looks good or is unusual or wanted, will trade you their stock for your potted-up things, at wholesale prices, while you pay retail, of course!

Any smaller shrubs for my zone that tolerate wet especially melting snow runoff and freezing and thawing? Pussywillow I don't want near the sewer water lines which this spot would be somewhat.