I would like to transfer the symbology from my ArcGIS online maps to desktop. Each time I download it reverts to default.
Does anyone know of a way to do this, or perhaps there is a symbology package I need to download?
First select "Open in ArcGIS Desktop":
Once open on your desktop select the layer you want to export:
Once you have exported the data open its properties and choose to import symbology from the layer you just exported:
You should now have the layer symbolized as it was in the web map, if you already have the data saved locally you can skip step two and just import the symbology. Also as Chris W pointed out in the comments you could also just save as layer file and use that to load the symbology.