As far as I know, there is no way to send pictures through messages. You can certainly send links through messages, so if you have a place where you can upload images to be seen on the net, then you can send the links to your trading partners.
You can also trade e-mail addresses and send that way, if your trading partner is agreeable to giving out their e-mail address (I know I have no problem doing that).
-- Dan --
Note: Please see my profile for more info regarding trading (section updated 3/4/2024). I have added a large portion of my inventory to the site, and currently have trading turned on (details are in my profile).