I've already posted one answer, but I found an effective and simple solution, though it does have a few side effects.
If you open the Window Color and Appearance settings, and select the "Window" item, you can change the default background color for application windows. This will affect the background color of the Preview Pane and of emails you are composing, as well as a few other UI elements, such as (I believe) the Quick Steps box in the ribbon. Pretty much anything in Office 2013 that's still stark white, even when you choose the so-called "Dark Gray" theme, is going to be driven by this system color.
The side effects I mentioned are that this setting will also affect a number of other UI elements in numerous programs. So while you might be tempted to choose a color like a medium gray (like the scrollbar in the above screenshot), you will likely find this causes other things, like Excel, Notepad, or "Options" dialog boxes, to be far too dark. I actually went with a color very close to white - RGB 252/252/252 - and that was dark enough to eliminate the "blinding" tone of Outlook 2013 without compromising the readability of other programs.
This will work in Windows versions up to 7; I'm not sure exactly when Microsoft removed this dialog, but it's definitely not accessible in Windows 10 version 1709. If you can't access the Window Color and Appearance dialog in your version of Windows, you can also manually adjust the associated registry keys as described in this answer, but this approach will require a logoff and logon in order to apply the change.