“Reindeer” sounds like “rain, dear.” ““Santa Claus is welcome but I do not want to see the rain dear” was printed in an 1888 newspaper. “Why does Santa Claus like the clouds? Because he keeps the rain, dear” was printed in 1895.
 
“Rudolf the Red knows rain dear” was printed in a 1953 newspaper. Another “rain, dear” version was posted on the newsgroup alt.fan.jen-coolest on December 14, 1998:
 
“ObOldCrimboJoke: Santa asked Mrs Clause to look out the window and see if it was snowing yet. Her reply: ‘Looks like rain, dear.’”
 
         
26 December 1888, Manning (SC) Times, pg. 6, col. 1:
“It is tome for Santa Claus,” said the young wife. “Yes,” said the spouse, who kept a retail store. “Santa Claus is welcome but I do not want to see the rain dear.”
 
25 December 1895, Chicago (IL) Daily Tribune, “In a Minor Key,” pg. 12, col. 6:
Here It Is Again.
Laura—“Well, Santa Claus will have no use of his sled this year.”
George—“Why not? Doesn’t he come with the rain, dear?”
 
25 December 1895, New Berne (NC) Daily Journal, “Xmas Conundrums,” pg. 1, col. 2:
Why does Santa Claus like the clouds? Because he keeps the rain, dear.
   
4 December 1931, Great Falls (MT) Tribune, pg. 5, col. 8:
IF THERE IS NO SANTA CLAUS—
Who Drives the Rain, Dear?
(That ought to hold you for a while.)
 
19 April 1953, Minneapolis (MN) Sunday Tribune, This Week magazine, “The Cerboard” by Bennett Cerf, pg. 4, col. 2:
FROM THOMAS F. HILL, of the “Birmingham (Ala.) News”: A high Soviet Commissar named Rudolph Mozoltoff was walking down a Moscow street with two friends—a man and his wife—when a drop of moisture settled on his blouse. “It’s raining,” he announced through his beard. “You’re wrong,” said the wife. “It’s snowing.” “Oh, no,” insisted her husband. “Rudolph, the Red, knows rain, dear.”
 
25 December 1984, Palm Beach (FL) Post, “Cryptoquips,” pg. B11, col. 1:
THE WEATHERMAN’S VIVID FORECAST TO WIFE ON CHRISTMAS EVE: “RAIN, DEAR.”
     
Google Groups: soc.culture.nordic
Greenland claiming residence of Santa Claus
Pekka Ahonen
8/28/92
(...)
Rudolf the Red knows reindeer 😉

(No flames, this wasn’t quoted straight from “America’s Funniest People”, because in that show the joke went something like this:
 
A Russian man called Rudolf looked out of the window and said to his wife: “Soon it will be raining”. His wife said: “How can you say like that? The sun is shining and there are no clouds in sight”. Rudolf answered: “Rudolf the Red knows rain dear”.
       
Google Groups: alt.fan.jen-coolest
Sunny Skies
Simon Lamont
12/14/98
(...)
ObOldCrimboJoke: Santa asked Mrs Clause to look out the window and see if it was snowing yet. Her reply: “Looks like rain, dear.”
 
Google Books
The Man Who Loved Christmas
By Kathryn Shay
Harlequin Books
1999
Pg. 289:
‘What did Santa say to Mrs. Claus when asked about the weather?” Quiet. “It looks like rain, dear.”
   
Google Books
1001 More Cool Jokes with Glen Singleton
By Barb Whiter
Victoria, Australia: Hinkler Book Distributors
2002
Pg. 139:
What did Santa Claus’ wife say during a thunderstorm?
“Come and look at the rain, Dear.”
   
Google Books
Christmas Around the World
By Emily Kelley
Minneapolis, MN: Millbrook Press
2004
Pg. 43:
Q: What does Santa Claus say to Mrs. Claus when he looks out the window?
A: “Looks like rain, dear!”
     
Twitter
C_w_D‏
@HollywoodIC
“I ain’t Santa Claus, but I make it rain dear…” - Lil’ Wayne
8:40 AM - 8 Jul 2009
   
Twitter
Products&Services‏
@opportunn
What did Santa Claus’s wife say during a thunderstorm?
‘Come and look at the rain, dear.’
http://p.gs/ahuuf
2:36 PM - 24 Nov 2009
 
Google Books
Christmas Cracker Jokes
By Amanda Li
London, UK: Macmillan Children’s Books
2014
Pg. ?:
What did Mrs Claus say to Santa Claus?
‘It looks like rain, dear.’
 
Twitter
Bumbly1uk.com‏
@CliveDavies15
CHRISTMAS CRACKER JOKES
—————————
What did Santa say to Mrs. Claus when he looked out the window?
Looks like “rain”,  “Dear”
—————————
SOON BE CHRISTMAS
YouTube : bumbly1uk 🎄💖🎄
7:12 AM - 1 Dec 2017