When I open a webmap in ArcGIS Desktop from ArcGIS Online, it displays all 4 layers of my feature service as turned on, whereas I actually have them all turned off in the saved webmap in ArcGIS Online.... I'd like them off by default because they are large datasets and I also have a tiled version of the service in the map for quick visualization. If the feature service is automatically turned on as soon as the webmap is opened in ArcMap then it sort of defeats the purpose because the map is super slow to open. I contacted ESRI tech support after no one responded to my GeoNet question and this was logged as a bug; BUG-000104595 : All layers from a web map are checked in when opened in ArcGIS for Desktop though some layers are unchecked in the web map.
I think that this is a high priority and needs to be addressed asap.