Current situation and outlook
The Alps are in a northerly flow that could have come from the dreams of the Powder Oracle. The decisive factor for the development was the build-up of the Azores High off the European Atlantic coast. The high "blocks" the Atlantic and disturbances have to move northwards before they make it to the Alps or Central Europe. Downstream (east) of the high wedge is the counterpart of the wave: a high-reaching low that taps into cold polar air and steers moist, cool air towards the Alps. Over the next few days, the axis of the high will increasingly tilt to the east, so that the north-easterly flow will become a north-easterly flow. The air masses brought in by this will then tend to be drier than recently, but somewhat colder.
The main snowfall is likely to have ended yesterday (Tuesday), but it will continue to snow in congested areas today and in the coming night. On Thursday, the chance of clearing is higher during the day, but it won't be completely sunny in the north. Friday will look pretty cloudy again, with snow showers on and off. Even if it snows down to low altitudes, it's still March and that means that the sun will be comparatively strong and the powder will quickly lose its fluffiness if it does break up briefly.
South of the main Alpine ridge, things look very different: Here it's fluffed up with north föhn and away from the main ridge there has been little to no snow. This situation will not change significantly over the next few days, and it will also tend to get a little cooler in the south due to the rotation to the NE.