CapriUni,
"Mele Kalikimaka" is the thing to say on a bright Hawaiian Christmas Day.
That's the island greeting that we send to you from the land where palm trees sway.
Here we know that Christmas will be green and bright,
Sun will shine by day and all the stars by night.  ...

Just to let you know there are songs about Christmas that don't mention snow.

(I do get a lot of requests for "Jingle Bells" when I do Christmas programs down here in San Diego, though.   One of the up sides of doing gigs at retirement and nursing homes and senior centers is that the folks are still into Christmas music at least until New Year's Eve, so I get to keep my Christmas repertoire going a bit longer.)

A related rant:
Why do we have to stop singing "Jingle Bells,"  "Baby, It's Cold Outside," and "Let It Snow!" after Christmas?   Those songs have nothing to do with Christmas, and in most places I've lived or travel in, we usually get our coldest, snowiest weather in January and February!

G