Daisy,
Assuming it's physically possible to paint the "plastic wood", I would
hesitate to do so unless you, or someone you know/hire is a very good painter.
Nothing looks worse that a "half-ass" attempt at "oriental-looking"
painting.... You can do a lot with fabric (curtains, sofa covers, wall
hangings, etc) to give your trailer an "Oriental" look.
On a side note, I saw a PBS special on the story of that house. How they
found it, purchased it, disassembled it, shipped it to the US and
reassembled it. They shipped over Chinese craftsmen to supervise the work,
using native tools and techniques as much as possible. They also observed
several customs and traditions, performing traditional ceremonies, etc.
Looking forward to seeing you again in Niagra Falls....
Dave