I agree with @Andy Homan. The Tell-a-Friend option will work for you, but because of your set-up you will need to secure it well. This is a prime opportunity for spammers to use your server, for sending spam. There is some leeway, if your members are also restricted to just real life members of your organization. But that won't stop someone from being gung-ho about marketing themselves or their work to as many other people as possible. So be forewarned.
That said, we use the Tell-a-Friend form for a number of things in one of our client's set-up. They wanted to be able to send full text of letter-writing campaigns to both the writer, local politicians, and keep an internal copy. This was before add-ons like 'PostMaster' by ObjectiveHTML. And 'Tell-a-Friend has served us well.
If you have a lot of members, you'll probably want a method for the user to select which members to send to. This could possible be ajax type ahead on the member list or maybe the Chosen Select plug-in or VMG Chosen Member, but otherwise, the form should work well.
Just a note about security, because having your website blacklisted as a spammer is no fun. Make sure ONLY members can access the form. See if you can limit the number of emails per hour or only 1 or 2 per 15 minute period. Track outgoing emails with a service like Mandrill or another service. This will allow you to see if a user us targeting the full membership list. Also, if possible, figure out a way to allow for members not to receive mail, from other members.