as far as i know,
the reason for "arms" in pub names has nothing to do with limbs.
it is more about heraldic coats of arms.
so, for example,
a pub called "the bricklayer's arms" was so named because all the local bricklayers got together and drank in there.
nothing to do with their limbs,
just the coat of arms they recognised.
"the royal arms" was where the royalists met for a drink and that.
et cetera.
a long time ago,
14th century at a guess,
pubs were told to distinguish themselves from normal dwellings by having something outside that would become recognisable.
so, for example, a landlord who wanted to attract farmers would put an old plough outside his inne.
hence, over time, it became known as "the plough".
from that advancement came the next...
swinging pub signs.
people couldn't read so much,
a mere painting of a plough was sufficient.
when people began to become more literate the name was also written in words,
but the painting still remained,
as it often does nowadays.
that's what someone once told me, anyway.