..I'm seeing everyone on the ninth of September in '03

The year usage is around, though perhaps a bit quaint and/or dated. Stereotype: an old codger offers a remark equivalent to "...why, Ah remember the big hurricaine back in September of Aught-two..."

I've heard people use "first September" in all seriousness; generally they have been British-educated or trained. Never "first Ninth," though.

Afterthought: in the present context, is there a difference between an "article" and a "particle" ?