Email them some pics with questions. Click onto their historic timeline.
http://www.woodard-furniture.com/
Sonny

Woodard's response to my email querry...

"Unfortunately we do not have any records of the furniture Woodard
made pre-1930s. Based on the metal plaque inside the furniture, what
you have is from the Woodard company, but it is unlikely it would have
been painted originally. Someone who owned it at some point painted it
or had it painted. And because we don’t have records on the wooden
furniture, I cannot confirm for you what wood was used. To get more
information on the furniture, you might contact a local appraiser or
antique dealer."

Ergo, yes it's Woodard and no, we know nothing about it.