Koch avoided the horrendous morning weather -- which forced fellow Swede Annika Sorenstam to miss the cut -- and shot her second straight 4-under-par 68 to match Kung at 8-under 136.
"I putted really good for two days now," said Koch, who birdied four of the final six holes. "Not making everything, but everything is close and everything is a good speed."
Kung, the first-round leader who opened with a 7-under 65 on her 21st birthday, had three birdies and three bogeys, including one at the 18th that forced her to settle for a 71.
"Everything was in control, and then the wind started picking up on probably our sixth hole," the rookie said. "And all of a sudden, it got really cold and I just lost control of my drives."
Sorenstam, the top female player in the world who won six of her first 14 starts this season, could not control anything. She followed a 73 with a 77 and missed the cut for the first time in 75 events.
"I'm disappointed," said Sorenstam, a three-time Player of the Year. "I just didn't play well at all."
Some of the other big names remained in contention. Australian star Karrie Webb had two eagles en route to a 71 and was tied for third at 7-under 137 with Tina Barrett, rookie Beth Bauer and Paula Marti of Spain.
"I feel so happy to get in at 1-under par," Webb said. "I fell pretty lucky to do that. Obviously, two eagles in the round helped that."
Elisabeth Esterl was seventh at 138, a stroke better than a group of nine players that included defending champion Se Ri Pak of Korea.
Cold, windy conditions forced a number of high scores, including Juli Inkster's 78 that caused her to miss the cut at 9-over 153. Britain's Laurie Davies bogeyed the 17th hole and double-bogeyed the 18th, missing the cut by three shots.
"We hit the really hard holes at the wrong time," said Davies. "It was tough."
Koch did not have such problems, working around her bogey at the 11th hole with birdies at the third, 11th, 13th, 14th, 16th and 17th. She played in the afternoon, when the wind died down.
"For me, it wasn't too bad," she said. "When I looked out the window this morning, I thought it was going to be worse. I had good warm clothes on and it wasn't too bad."
Kung suffered in the morning cold and wind, playing the sixth through 11 holes in 2-over.
"I couldn't even write," said Kung, who attended USC and still lives in California. "My hands were shaking when I was writing on the yardage book. It was horrible."
Kung began the day with a one-stroke lead over Webb and quickly birdied the second hole and eagled the third. But she missed the green with her third shot at the par-5 seventh and pushed her drive at the par-4 ninth, bogeying both.
En route to her second bogey, Kung hit a young fan on the hand with her drive. The boy received medical attention, but suffered only bruises.
"I felt so bad," said Kung, who rebounded with a birdie at the 12th hole.