Distance blurring is an effective technique to cover up the inconsistencies of distant objects, and to present a “real world” feel to distant objects.
In order to achieve this you need to render your scene to a Texture instead of the screen (deferred rendering) and pass that Texture through to a XNA SpriteBatch (i.e. render it in 2D) with an attached pixel shader to blur the colours.
In order to blur the colours based on relative depth from the current perspective the pixel shader should sample the depth buffer (recorded in an another Texture generated during deferred rendering and passed into the blur shader)
This technique is similar to attenuation where the colours are allowed to fade out but affects the sharpness of edges as well. Distant objects blur together slightly out of focus.
The pixel shader pseudo-code can be found here http://xboxforums.create.msdn.com/forums/t/7015.aspx.
Trees softening into the distance. To get double the blur effect, just run the shader twice.