Who is the female artist who sings "Sleigh Ride"?

The radio station website doesn't have their Christmas playlist up, but it's probably one of these:

1950 - The Andrews Sisters - notable as the first known vocal recording.
1956 - Jo Stafford - Ski Trails
1960 - Ella Fitzgerald - Ella Wishes You a Swinging Christmas
1963 - Ronnie & The Ronettes - An altered version with background vocals singing "Ring-a-ling-a-ling Ding-dong-ding" and excluding the lyrics "giddy up giddy up let's go" and "The birthday/Christmas party at the home of farmer Gray."
1970 - The Carpenters
1977 - The Mormon Tabernacle Choir (and again in 1982, 1987, 2005, and 2006)[3]
1992 - Debbie Gibson - A Very Special Christmas 2
1993 - Amy Grant - A Christmas Collection
1996 - Spice Girls - B Side of "2 Become 1"
1997 - Lorrie Morgan - Merry Christmas from London
2000 - Vanessa Williams - from the movie A Diva's Christmas Carol
2001 - TLC - MTV TRL Christmas
2002 - Hillary Duff - Santa Claus Lane
2004 - Play - Play Around the Christmas Tree
2007 - KT Tunstall - A target exclusive CD

I'm not sure if this is who you are looking for but singer Amy Grant sings a very nice rendition of Sleigh Ride.  Coincidentally, I was looking for Christmas songs on Itunes the other day and came across her version of the song....very nice.

Given your description, I am guessing that you are talking about Ella Fitzgerald's version of the song.  It's really good, one of my favorites.  It's on the album Ella Wishes you a Swinging Christmas but it's also on a lot of compilations since it is such a popular version of this classic song.