Platform(s): web browser, maybe Flash?
Genre: I forget. Possibly an adventure game?
Estimated year of release: I don’t have any idea on a release year, for all I know it was made in 1996 and survived till 2009! All I know is I played it somewhere between 2005–2009, giving 2009 as a hard upper bound on release year.
Graphics/art style: 3D cartoonish
Notable characters: Playable character was a Christmas elf, I think with blonde hair. Red and green outfit. Cannot remember the elf’s gender. I remember no other characters.
Notable gameplay mechanics: If I recall correctly you could walk between rooms and probably needed to find some object or other.
Other details: Spent a lot of time on sites like www.santafun.net, might have existed on some site whose name was some permutation of the words “santa” “christmas” “fun” “games”.
kinda shot in the dark, but maybe one of the Merry Gear Solid -games? https://static.wikia.nocookie.net/metalgear/images/9/91/Merrygear2.png
edit: I realize you said it was 3d, but… still giving this a go as a guess :P
Nope, but now I have to look into Merry Gear Solid haha