A snowman usually has a carrot for a nose. A popular joke (cited in print since at least 2002) has two snowmen standing in a field. One snowman asks the other, “Do you smell carrots?”
 
The joke has been printed on many images.
     
 
Wikipedia: Snowman
A snowman is an anthropomorphic snow sculpture often built by children in regions with sufficient snowfall. In North America, typical snowmen consist of three large snowballs of different sizes with some additional accoutrements for facial and other features. Common accessories include branches for arms and a rudimentary smiley face, with a carrot standing in for a nose. Human clothing, such as a hat or scarf, may be included. Low-cost and availability are the common issues, since snowmen are usually abandoned to the elements once completed.
         
Google Groups: alt.sports.soccer.sunderland
Baki Mercimek
Bobby
12/18/02
oh for foox sake! 😊
2 snowmen in a field - one says to the other “Can you smell carrots?”
me favrit at the moment.
   
Google Groups: alt.uk.noseypakers
Joke thread
The Man With No Idea
12/18/02
I think this is an old Peter Kaye one but it tickled my fancy:
Two snowmen in a field and one askes the other, “here, can you smell carrots?”
 
Google Groups: alt.happy.valley
Snowmen
Rabbit
11/19/03
Two snowmen in a garden.
One turns to the other and said ” Do you smell carrots” 😉
 
Runner’s World (UK)
M…eldy
7/12/2003 at 23:47
Two snowmen stood on a hill….
One said to the other
‘can you smell carrots’??
 
Google Groups: alt.music.mp3.winmx
Christmas Joke
Chrome Boy
12/23/04
Two snowmen are chatting…
First Snowman: “Can you smell carrots?”
 
Google Books
Finding Lost:
The Unofficial Guide
By Nikki Stafford
Toronto, ON: ECW Press
2006
Pg. 174:
Interesting Facts: There are two common answers to the riddle that Desmond poses to Locke (What did one snowman say to the other snowman?): the first is “Freeze” and the second is, “Do you smell carrots?” Not exactly rotflmao, but cute.
 
Google Books
The Giant Bathroom Reader
Edited by Karl Shaw
London: Constable & Robinson Ltd.
2006
Pg. 304:
Joke of the Day
One snowman to another: “Funny, I smell carrots, too.”
 
Google Books
February 2006, Boys’ Life, “Think & Grin,” pg. 53, col. 2:
William: What did one snowman say to the other snowman?
David: What?
William: Do you smell carrots?
William David Wade, Shapleigh, Me
 
Twitter
Kalamazoo Gazette
‏@Kzoo_Gazette
TODAY’S CHUCKLE: What did one snowman say to the other snowman?: “Do you smell carrots?”... http://tinyurl.com/2sy3qr
6:40 AM - 14 Mar 2008”
   
Google Books
The Mammoth Book of One-Liners
By Geoff Tibballs
London: Constable & Robinson Ltd.
2012
Pg. ?:
Two snowmen were standing in a field. One looked at the other and said:
“Can you smell carrots?