It's a time + association thing. Horns were used more in music than stringed instruments (read: guitars) for decades. You still hear a lot of horns in early rock and roll/adult contemporary songs from the 50s. A lot of the earlier, popular "pop" Christmas songs boomers and gen-x grew up hearing either had the sounds of the 40s or the 50s so they want to emulate that when making their own songs. After that, it just kind of gets associated with the Christmas sound.