Many rock guitarists in the seminal '50s and '60s brought skills from other musical areas. In the '50s, for example, Scotty Moore was a country player who helped define the new rock genre.
But in the early '60s, folk, and by extension country, had a big influence on the developing rock sound. Jerry Garcia of the Grateful Dead, for example, started off as a country player:
Between 1962 and 1964, Garcia sang and performed mainly bluegrass, old-time and folk music. One of the bands Garcia was known to perform with was the Sleepy Hollow Hog Stompers, a bluegrass act. The group consisted of Jerry Garcia on guitar, banjo, vocals, and harmonica, Marshall Leicester on banjo, guitar, and vocals, and Dick Arnold on fiddle and vocals. Soon thereafter, Garcia formed a jug band, inspired by the Jim Kweskin Jug Band, called Mother McCree's Uptown Jug Champions, whose membership also included Ron "Pigpen" McKernan.
Many of the giant contributers from the '60s are irrelevant today. In some cases, due to death, in others, due to their coasting on their reputation.
But one who has returned to his roots, while retaining all his prodigious skills, is former Jefferson Airplane guitarist Jorma Kaukonen. From his website:
He was a founding member of two legendary bands, The Jefferson Airplane and the still-touring Hot Tuna, a Grammy nominee for his highly acclaimed “Blue Country Heart,” and the most in-demand instructor in the galaxy of stars who teach at the guitar camp that he and his wife operate in picturesque Southeastern Ohio.
His wonderful solo acoustic "Embryonic Journey" was on the first real Jefferson Airplane album (sorry folks, the Signe Anderson Airplane was transitional at best). It showcases not only great guitar skills, but a melodic sense that is still captivating.
Here's Jorma playing "Embryonic Journey" when the Airplane were inducted into the R'n'R Hall of Fame in '96, with some nice still photos:
And here's Jorma's electric side back then: