Who is the singer at the dance?

The singer's name is Don Walser, and yes, he is terrific.

The album 'Rolling Stone From Texas' has his version of the song, which is called "I'll Hold You In My Heart ('Til I Can Hold You In My Arms)."

Having cut my teeth on Bob Wills from 1937-42, when he was at Tulsa and created Cains Academy, while dominating Middle-America's Swing Band world -- then leaving the KVOO radio franchise, Cain's and the entire Texas Swing market to little brother, Johnnie Lee -- I'd love to go along with the one idea that the Hi-Low bar band was the Texas Playboys.
Actually, in that period -- there were hundreds of Texas Swing/Western Swing bands from Canada to the Rio Grande, from Ohio and Tennessee to New Mexico,Utah and Montana. Possibly the best single western swing band I've seen since the 70s was "THE SHERIFF WILLIE BROWN" playing out of Great Falls, Mt. in the 80s, headquartered in a really nice "tonk" along the east side of the State Fairgrounds.
Johnnie Lee Wills had the longest lasting scheduled TV show in the country on KVOO-TV, while continuing the KVOO radio schedule and weekly dances at Cains, until 1969. The original, "Take it away, Leon" -- Leon McCullife had his group at Tulsa headquartering out of KTUL and the Cimarron Ballroom, while Hank Thompson headquartered out of Oklahoma City and the Trianon Ballroom. Johnnie Lee had the huge advantage with KVOO's clear channel 50,000 watts which covered the entire middle of the continent.
Those three retired the same week in 1969 and "Rocky and the Shotguns" became the KVOO western swing band, with Rocky Caple on steel, Billy Walker most often fronting on vocals. Leon, Hank, and Johnnie Lee were all frequent guests on the TV shows. Charlie Pride made his first tour in that region with Rocky, who had the top instrumental on the West Coast with 'SAWED OFF SHOTGUN" until he retired about 1979-80. Leon came back with the Original Texas Playboys for concerts, appearing on AUSTIN CITY LIMITS at least once.
Bob and Johnnie Lee's youngest brother, Billy Jack created commercial Rock and Roll, with Tiny Moore heavily involved in creating early arrangements, in the 1942-55 era at Wills Garden, northeast of Sacramento. As Bob burned out in the early 50s, largely from his long-time alcohol problems, he returned to Wills Garden and as big brother, just "took over." That great band quickly disbanded, Billy Jack moving to Okmulgee, OK where he bought a plumbing business and continued playing dances into the 1990s. Brother, Luke Wills and his Rhythm Wranglers were a steady lounge act group in Las Vegas for decades.
Bob eventually was leading a chain of pick up bands and playing Texas "tonks" for as little as $300 per night. In the 30s and 40s, into the early 50s, Bob Wills and the Texas Playboys were the HIGHEST EARNING BIG BAND OPERATION in the country.

Don Walser was the singer you asked about. Like you I was reading and watching the movie at the same time when I heard Don singing. He knocked me out. I immediately bought the sound track and all of his CD's. Don was from Brownfield, Texas and was in the Texas National Guard for many years. He was the best yodeler I ever heard and was known at the Pavarotti of the Plains. Sadly Don passed away in 2006.

I just saw the movie for the first time. The song "I'll Hold You in My Heart" was a big hit for Eddy Arnold in the 50s.He also wrote it.

Don Walser, I bought all his records. He is really good. He died, not sure the date was. But he had complications with Diabetes. You can find his music on Amazon.com. He got such great reviews they asked him to be on the "Grand Ole' Opry.