For my money, Sammy Davis Jr. and Carmen McRae recorded the definitive version in 1957.
First, a couple that performs "Baby, It's Cold Outside" has to have chemistry for the song to work. Willie Nelson and Norah Jones sang this duet in 2010, and they're both great performers, but there's 46 years between their ages. That's kind of gross. Plus, it doesn't sound like they're even in the same room. In contrast, Sammy and Carmen sound like they're sharing a microphone, and singing arm in arm.
Secondly, the song is suppose to be playful. There's a reason performers have had fun playing the roles. John Travolta has sang the mouse to Olivia Newton-John's wolf. Once Bing Crosby and Jimmy Stewart sang this together on the radio, with no female mouse stirring in the house. When you listen to Sammy and Carmen play off of each other, it really does sounds like play. You can't tell me they're not having fun. By the end, they're both goofing and laughing.
Thirdly, there's Mr. Davis. I really enjoy how Sammy's vocal delivery romps around within the parameters of the lyrics, "Look. Out. That-a Win-dow A-at That Storm." And I'm sure it's just my imagination, but I swear I can hear the ice in his Manhattan clinking as he's swings the glass around.
Link: Baby It's Cold Outside