Nope, never heard of them. GuideStar (a web listing of 501c3
charitable non-profits) indicates they do not file form 990
with the IRS, so their annual income is tiny. And they have
moved between states, and not in high areas of high profile
for lobbying, so I suspect it is a 1-person labor of love.
AMEA has produced a newsletter since 1993 (or before). Until
2002, the AMEA website was hosted on Bob Dawson's equine law
web site (http://www.law.utexas.edu/dawson/amea/amea.htm), and
the newsletters from 1993-2002 are still there. They are an
interesting read.