Hi Bonnie and thanks for sharing your story. Certainly this is only my interpretation, but do note I didn't label Rudolph as gay! I see him as queer, standing outside the status quo and being rejected by his peers. Who he “collaborates” with, Hermey and Cornelius, are highly suggestive of some parts of gay culture.
Just for fun, if you try and take a similar read of Frosty the Snowman, you just don’t get the same outcome! :-)