Dortmund took three points thanks to second-half goals by defender Neven Subotic and midfielder Mario Götze to keep the champions fourth, nine points behind leaders Bayern Munich who host Bayer Leverkusen on Sunday.
Players from both sides struggled in the icy conditions as Klopp's team got back to domestic business after their shock 2-1 win over Real Madrid on Wednesday in the Champions League.
"In the good old days, your mother wouldn't allow you to go out and play in weather like that, but we had to go out and get on with it," said Klopp.
"My team gave another outstanding performance and showed their character and passion in very difficult circumstances, I am very proud of them."
Having trained for the Real game in "t-shirt weather," Klopp admitted the heavy snow on the pitch had forced him to abandon a passing game for a more aerial approach.
Having dazzled Madrid with slick dribbling, Dortmund had to bide their time and wait for their chances against Freiburg. "We hadn't expected the snow would stick," said Klopp. "If the ball doesn't roll, then it has to fly."
Dortmund are at second-division VfR Aalen, again in south-west Germany, in the German Cup on Tuesday.
"I hope they have undersoil heating," said Klopp.
While Dortmund battled the weather, Schalke 04 went second in the table as they backed up Wednesday's 2-0 win at Arsenal in the Champions League with a 1-0 win at home to Nuremberg in Gelsenkirchen.
Schalke also had to labour for their three points as Peruvian striker Jefferson Farfan hit the only goal of the game in the 77th-minute.
"We were motivated to win and the coach had talked about the need for a good performance after London," said Schalke goalkeeper Lars Unnerstall.
"We want to stay up there, to stay in touch with Bayern and we want to make sure of our Champions League place."
Eintracht Frankfurt can regain second spot from Schalke if they win at Stuttgart on Sunday afternoon.