Why are the options given for IconData causing errors when used?

From the above comments and some inspection we find that according to the decisive authority of the documentation using Options for IconData is not supported. Using Trace we see that IconData uses DataPaclets`IconDataDump` which will not make use of the options given in a way we want.

One work around is to use ReplaceAll for the Graphics object returned by IconData (a careful inspection using FullForm will tell you what to replace):

IconData["WindDirection", 315] // ReplaceAll@
    {
        Rule[Background, None] -> Rule[Background, Green],
        Rule[ImageSize, __ ] -> Rule[ImageSize, Large]
    }

An alternative work-around is to take the graphics primitives returned by IconData and use them in Graphics with desired options added:

Graphics[First @ IconData["WindDirection", 315], 
 Background -> Green, ImageSize -> Large]

Per my comment, if you look at InputForm@IconData["WindDirection", 315], you'll see that it returns a Graphics object.

Thus a sensible workaround would be:

Show[IconData["WindDirection", 315], Background -> Green]

since it will act like any other Graphics object.

For instance, you would also be able to use DiscretizeGraphics and its ilk:

The natural Wolfram order of things is that if a symbol or something about a symbol is not documented, it's not officially supported and is likely to change, stop working, or exhibit weird behaviour (as in your case).