No sweat for Kaepernick. He went sleeveless, and didn't wear gloves.
"I've played in cold-weather games before," he said. "I feel like it's more mental than anything."
San Francisco plays at Carolina next Sunday in the divisional round.
In a back-and-forth fourth quarter, the 49ers (13-4) threw the final punch. Kaepernick escaped a blitz to get to the 27 with 1:13 left.
"Just trying to figure out a way to get that first down," Kaepernick said. "Had a play called, we didn't get the look that we wanted. It worked out for us."
"Very disappointing, personally," Rodgers said. "It's frustrating not to play your best game in tough conditions. Defense holds them to 23 points. We should win that game."
But it was Kaepernick who was the difference-maker once again in San Francisco's fourth straight win over Green Bay. He finished 16 of 30 with the touchdown and an interception.
"I'm just very proud of this team as far as their ability to continue to overcome adversity," coach Mike McCarthy said. "It hit us at every turn, it hit us again today and these guys just keep fighting and fighting."
In a memorable playoff debut last January, Kaepernick ran for a quarterback playoff-record 181 yards and a pair of touchdowns. In the season opener in September, the strong-armed quarterback threw for a career-best 412 yards and three scores.
This time, he did his damage on the ground and through the air.
Kaepernick tore through the Green Bay defense for a 42-yard run, getting a break at one point after House whiffed on a tackle, to set up Gore's 10-yard touchdown run that helped give the 49ers a 13-10 halftime lead.
"It was unbelievable, the way he was getting the edge. I mean, just clutch," Harbaugh said. "Colin Kaepernick, I think we can all agree, is a clutch performer."
Notes: It was the seventh-coldest game at Lambeau Field since 1959, and the fourth-coldest postseason game at the stadium. ... Kuhn has scored a touchdown in each of the last five postseasons. ... After a big day in the season opener against Green Bay, Anquan Boldin was held to three catches for 38 yards.
Copyright 2014 by The Associated Press