Ask Mr. Smarty Plants

The USDA Plants Database shows that Styrax grandifolius (Bigleaf snowbell) is listed as "Endangered" in both Illinois and Indiana and "Presumed Extirpated" from Ohio.  It occurs in several counties in extreme eastern Texas and eastward through Arkansas and Louisiana to Georgia, Florida, South and North Carolina and north to Indiana, Illinois and Ohio.

One study, Conservation Assessment for the Bigleaf Snowbell (Styrax grandifolius Ait.), by Steve R. Hill from the USDA Forest Service, Eastern Region, says that there nothing is known about the the seeds longevity and whether they persist in the soil seed bank.  The study doesn't give germination information for Styrax grandifolius, but does give it for a related species, Styrax japonicus, that says that this species germinates best if it receives one month of warm stratitification and two months of cold stratification but they don't offer temperatures for either stratification.

The Randy Stewart Landscape Design blog says that Styrax species usually need stratification to easily germinate.

Garden Guides says that cold stratification is NOT required. 

The Permaculture Research Institute has instructions on How to Germinate Your Seeds that gives instructions for stratification.  Germination Instructions for Seeds from Wild Ones has more information on stratification.  Schumacher Tree & Shrub Seeds talks about warm stratification in How to Treat Seeds.

If you have plenty of seeds, you might do your own experiment for germinating them by trying some with cold stratification, some with warm stratification and then cold stratification treatments and some with no stratification.