Keep your letter exclusive to one newspaper.
Exclusive content is what gives each newspaper its unique character. So editors publish content that hasn’t been published anywhere else. The letters to the editor page is no different.
Sending one letter to several newspapers is like dating two girls simultaneously. It betrays the the expectation of an exclusive relationship between the letter and the newspaper. It’s low-brow and wrong, even if the letter gets published multiple times at various papers and web sites.
This is also why many editors frown on letters CCed to long lists of family, friends, politicians, activists, organizations, or mailing lists. Including so many people in the correspondence turns an exclusive letter to the editor into something more akin to a public statement.
There’s nothing wrong with making public statements, but be honest with yourself. If your goal is to get your letter to the editor published, treat it like a letter and not a press release. Once you’re published, you’ll see the exclusiveness is worth it.