Good question. His obit and a short bio of him in one of those turn-of-the-century "leading figures of our community"-type books completely botch his CW career - whether this was done intentionally and/or by Woodson's direction is anyone's guess. I, and the only other historian to attempt to tackle Woodson's CW career, both think he may well have been trying to hide some early war guerrilla activities in MO.
I've never tried to track down the Compiled Service Record of anyone else in his company besides him, so I honestly don't know how well records were kept within his company. The editor of the Harrisonburg VA newspaper was quite fond of the Missourians apparently, but after New Market they drop off his radar.
And one thing that I find interesting too is that for a good part of its existence, Woodson's command was attached to the 62nd Virginia Mounted Infantry. The 62nd's Colonel, George Smith, was a prolific writer, particularly about the New Market campaign. Yet even Smith has little to say about Woodson. But that is just part of a larger problem of the dearth of reliable source material about Imboden's brigade from this time period.
Another possibility, and this is just conjecture on my part, is that perhaps Woodson wanted to keep a low profile. For whatever reason, he did not want to go back to the Western or Trans-Mississippi Theater, and there was at least one move by the War Dept - which took the intervention of RE Lee himself to prevent - to force Woodson and his command West. Perhaps he felt that staying out of official view would keep him in Virginia. But then this idea can be torpedoed by the spotlight shining on him with Early attempting to have his and McNeill's commands done away with, and by Woodson appealing directly to Sec'y of War Breckinridge to remain in VA.
Many more questions than answers when it comes to Woodson, unfortunately.