While it's now impossible to imagine anyone else other than Alex Kingston playing Professor River Song in Doctor Who, that was not always the case. According to BBC Books' Doctor Who: The Writer's Tale, series producer and writer Russell T Davies did not always have Kingston in mind to play the Doctor's wife. The book was published in 2008 and was based on an email correspondence between Davies and journalist Benjamin Cook, which started in February 2007 and lasted until March 2008, during the production of Doctor Who season 4.
Alex Kingston's River Song first appeared in the classic Doctor Who season 4 episode "Silence in the Library." Most of her appearances in the show took place in Doctor Who seasons 5-7 opposite Matt Smith's Eleventh Doctor when Steven Moffat had already succeeded Davies as lead writer, but her debut happened with David Tennant's Tenth Doctor. In full Doctor Who fashion, it also coincided with her death, as she chose to sacrifice herself to protect the Doctor and Donna Noble (Catherine Tate), as she knew the Doctor from his future—which was technically her past.
According to an email from Davies to Cook dated December 1, 2007, in The Writer's Tale, the first actor they thought of when debating who to cast in River Song's role was Titanic star Kate Winslet. In the email, Davies wrote that they were trying to get Kate Winslet to play Song, describing the character as "sort of the Doctor's wife" while also hoping to get Harry Potter's Michael Gambon or Ian McKellen for the role of Dr. Moon. Davies ended the email exclaiming, "Fat chance!" commenting on the unlikeliness of that to happen, and indeed, in the end, the roles went to Alex Kingston and Colin Salmon, respectively.
Although Winslet could have been thought an unlikely choice, especially as between 2007 and 2008 she was busy filming both Sam Mendes's Revolutionary Road and Stephen Daldry's The Reader, she had previously worked with Davies. In fact, her first-ever acting role was in the 1991 sci-fi TV show Dark Season, created by Davies for BBC One. In it, Kate Winslet played teenager Reet, one of the three pupils who, suspicious of Mr. Eldritch (Grant Parsons), wanted him removed from the school.
There is no explanation as to why Winslet wasn't cast as River Song in The Winter's Tale. The following mention of River Song was in an email from December 21, 2007, where Davies announced to Cook that not only had Alex Kingston been cast as River Song, but that he loved her for the role of the Doctor's wife. Although Kate Winslet would have surely been an excellent addition to Doctor Who, in the end, Alex Kingston prevailed, offering Doctor Who viewers her beloved version of River Song—bold, adventurous, and equipped with cheeky catchphrases such as "Spoilers!" and "Hello, sweetie" that cannot be detached from Kingston's stunning portrayal of the character.