I have downloaded the Blender 2.8 Alpha2 from the 21 September 2018.
There I tried to snap my object to the current visible grid. This was supported in 2.79. Also the documentation of 2.79 confirms the behaviour.
All the GIFS were made with factory settings. I hold CTRL for snapping while moving the Object. I made no changes to the settings or else.
So, does anyone know if this will be part of 2.80 later? Or is this change intentional?