CBS is running the 1964 special Rudolph the Red-Nosed Reindeer on Monday, November 22, 2021 at 8pm ET

It was written by Romeo Muller, who wrote for Jack Benny and started to make his mark in early television on programs like Studio One.

Muller wrote 12 Theater Five scripts, most likely written in 1964 when Rudolph production was in full swing getting ready for its debut. He probably wrote the Rudolph script in 1963.
110    1965-01-01    Discotheque
135    1965-02-05    The Underdeveloped Nation
142    1965-02-16    A Little Game on Saturday Morning
149    1965-02-25    Toby's Wonderful Egg
150    1965-02-26    Little Girl, Little Girl
172    1965-03-30    Bright House, New House
192    1965-04-27    Lorna is a Strange Child
195    1965-04-30    Make My Name Clean
202    1965-05-11    Nightmare at 26,000 Feet
217    1965-06-01    Mama's Girl
229    1965-06-17    Country Boy (NOMINATED FOR A WRITERS GUILD ANNUAL AWARD)
245    1965-07-09    Ed's War

More details about Muller can be found at
Wikipedia https://en.wikipedia.org/wiki/Romeo_Muller
Variety https://variety.com/1992/scene/people-news/romeo-muller-102463/

Wikipedia states "Muller read his favorite and first Christmas story every year on Christmas Eve on New York radio station WGHQ"
That was near where he lived, about halfway between Albany and NYC in NY
It's doubtful they were recorded by the station -- I've never seen an aircheck

Nice story about the puppets used in the special https://www.smithsonianmag.com/smart-news/holiday-season-you-could-put-rudolph-under-christmas-tree-180976131/
Muller himself was a young puppeteer when he grew up in Long Island

Muller may have also acted in T5. Tracking that down in the series research....

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For anyone that has a VPN the Rudolph classic is available at yts.am.   This was a unique classic that you can never get tired of watching.  Good old Burl Ives.  "Happy Birthday everyone" quote from another xmas classic Frosty The Snowman.