The 37-year-old Frost, a PGA assistant professional at Quail Hollow Club in Charlotte, N.C., eagled the par-5 16th hole on PGA Golf Club's Wanamaker Course. He matched Schmid at 8 under.
"I had just come off a bad bogey at 15 and needed a boost," Frost said. "I hit a nice 5-iron close and made the putt, which was huge. ... I feel good about my game and played really solid out there, all things considered. I'm where I want to be going into the final round. It's always nice to be in contention and really, that's the reason we practice so hard."
Schmid, a 45-year-old PGA assistant professional at Perche Creek Golf Club in Columbia, Mo., bogeyed his final two holes for a 74.
"I really only had a couple of chances on the front nine to make birdies and didn't take advantage of those opportunities." Schmid said. "It was a tough day out there overall with the wind. I didn't play all that bad, but it was a struggle figuring out where and how to hit the ball.
"If you put the ball in the right spots on this golf course, it isn't too hard. But if you put the ball in the wrong spots, you'll struggle. And that's what I did today."
Two-time champion Frank Bensel of Purchase, N.Y., was a stroke back after a 66. The 45-year-old Bensel, the PGA assistant professional at Century Country Club, had a bogey-free round.
"Yesterday, I didn't play that bad but the putts just didn't fall," Bensel said. "But today they went in. If you don't make bogeys out here and keep it in play, you can score."
Ashley Grier of Hagerstown, Md., the first female player in the event since 2011, was tied for 32nd at 4 over after a 76. She's playing the course at 5,941 yards, while the men are playing it at 6,971.
The tournament winner will receive $9,000 and a spot in the PGA Professional National Championship in June in Myrtle Beach, S.C.