Due to background-image being marked !important in the media section of re-com.css, all attempts to style this control via stylesheets with a custom image for the dropdown arrow are failing. I had to resort to the following 'deep hacking' in componentDidMount to achieve the styling.
(.setProperty (aget b "style") "background-image" "image.png" "important")
 
where b is defined as:
(.item (.getElementsByTagName (.getDOMNode this) "b") 0)
 
This poking into the implementation of the dropdown to pull out a b is obviously not ideal.
See Issue #99 for similar situation.