Outside of Ennio Morricone's (DOLLARS trilogy, OUATITW, DUCK, YOU SUCKER!, NAVAJO JOE), Elmer Bernstein's MAGNIFICENT SEVEN, Jerome Moross's THE BIG COUNTRY, Victor Young's (SHANE, CALL OF THE FARAWAY HILLS, JOHNNY GUITAR), John Barry's DANCES WITH WOLVES, Alex North's CHEYENNE WINTER, and Jerry Fielding's (THE WILD BUNCH, THE OUTLAW JOSEY WALES, CHATO'S LAND, THE LAWMAN), my favourite Western scores (and probably the most sorely overlooked by fans of the genre) are those of Jerry Goldsmith, in particular LONELY ARE THE BRAVE and THE HOUR OF THE GUN.
A few others worthy of mention.
And last but by no means least, arguably the most "authentic" Native American film score ever written. Apparently Rosenman stayed on a reservation, smoked a peace pipe and everything, as part of his research. Gives me chills every time I hear it.