I had lived in Huntsville for almost five years before discovering the Beaverdam Swamp boardwalk which is part of Wheeler Wildlife Refuge although at the far eastern edge. The trail is impossible to find unless you know about it and I'll tell you: very few people know about it.
If you're looking for a shaded trail suitable for strollers and wheelchairs but quieter than the Huntsville greenways, consider a trip to Alabama's largest Tupelo swamp. The raised trail runs about a mile into the swamp with several benches. Be careful after a rain as the moisture and lack of sunlight can cause the wooden path to become slippery with mold.
About five minutes into the trail, the sounds of interstate traffic fade and it's just you and the trees. And the birds. Beaverdam Swamp Boardwalk is part of the North Alabama Birding Trail and many woodpeckers and several other birds are common here.
For a short list of the plant and animal life offered, visit the Alabama Dept of Conservation and Natural Resources page devoted to Beaverdam Swamp.
The Huntsville Wildflower Society used to host wildflower hikes at Beaverdam Swamp looking for wetland flowers such as dwarf trillium and trillium pusillum. These hikes have not occurred in a few years probably due to the recent damage (see below).
In the past, Beaverdam Swamp was frequently the site of undercover police raids targeted at men exposing themselves and engaging in "inappropriate" activities1,2,3). Having said that, I haven't seen any news articles more recent than 2007 and there's rarely anyone there the times I've gone.
The storms in April 2011 destroyed large sections of the boardwalk. Huntsville Outdoors contacted park officials at Wheeler recently and were told that a contract had been awarded and repairs to the boardwalk "should begin within 2-3 weeks and probably take 2-3 weeks to complete after that." So by mid-late September, you'll be able to see firsthand what the heck a Tupelo is.
According to the same officials, the construction will involve repairing the damaged sections and removing trees that have fallen across the trail. They also plan to replace the entire boardwalk within the next 2-3 years.
For now, you can still walk the first half of the trail but I'd suggest staying in the center as some of the planks may be rotted.
The Beaverdam Swamp Boardwalk can be accessed by taking Old Hwy 20/Frontage Rd west from County Line Rd just south of I-565. Scroll down to see the map.