Actually, to my ears, "go seaward" sounds ever so slightly off. "Go seawards" sounds better. I'm among those people to whom "Xwards" suggests movement, while "Xward" is more suited to static orientation.
My dialect is mostly US southern mainland English, with scattered influence from many other places, including four years on O‘ahu. I have no idea where I picked up the "Xward/Xwards" distinction.
FWIW, The OED has citations of "the seaward" starting in the 14th century, "seaward" (no article) starting in the 16th century, and "seawards" (no article) also starting in the 16th century. Most modern dictionaries list "seawards" as an alternative form of "seaward".