I just bought a Bostitch 15 gauge finish nailer for some exterior trim
work. Bought some Bostitch nails. They say they're 'coated.' I
emailed Bostitch and they say the coating is not galvanized but just a
glue coating that helps in removal. They said to use stainless nails
for exterior.

Unfortunately the stainless nails are 4 times the price.

I presume I need galvanized nails for exterior work, right? I'll be
using this with both wood and PVC trim.

I may just return the Bostitch and get something else for which
galvanized nails are available.