Is this your Carrie?Combined info from TX Dth Idx Online 1964-1998 and SSDI:
Carrie P. Padgett, b 13 Feb 1887; d 17 Oct 1978 Wood Co, TX; last residence Mineola, Wood Co, TX; SS card issued in TX.
If so, you might look for an obituary for her.Maybe there will be something in it about her husband.Check Wood Co, TX GenWeb site, some GenWeb counties are putting their cemeteries online, maybe Henry is buried there with her.
Using the TX Dth Idx, and typing in just surname of Padgett and county of Wood, there are 10 listed.Since Padgett is not real common, I would certainly check out that county, and post queries on both the GenWeb and GenForum sites for Wood Co, TX.Once you find his date and location of death, you can obtain a copy of his death certificate, which should show the names of his parents. Happy Hunting (^_^)