Welshmen in the Civil War

There's a new website addressing the Welsh ACW experience, offering a selection of obits and letters. I see that Cadwallader is a Welsh name. I see also some things I cannot pronounce:
Abraham Lincoln had a grandmother who was a Cadwaladr, hailing from the Cerrigydrudion area between Llangollen and Betws-y-Coed.
Not many know a Cadwallader but everyone knows a coed.