You could use Aspect, as suggested by Dan to get the direction raster of the downhill slope.
Then use Extract Values to Points to transfer the cell values of Aspect Raster to the Point Feature class.
From symbology of the Point Feature, you may then rotate the symbol based on Aspect Attribute.

In my above example, I have also extracted the values of Slope Raster to the same Point features, and quantitatively classified (Graduated Color) based on Slope values.
Think Location