Can aircraft depart/arrive after another aircraft has sprayed snow on the runway?
Aircraft can land in snowy weather without a problem, the fact that there is a little bit of snow on the runway does not change that. The amount of snow can cause problems if it too deep and will interfere with the engines/landing gear struts etc.

The snow sprayed on the runway by the A380 is just a small film and no problem for aircraft to take-off and land on. The runway can become a bit more slippery decreasing the braking performance of the aircraft.