In the Alps, I don't expect fresh snow in the next four days. Until Thursday it will be dry everywhere. During the day the temperatures will rise, but at night it will still be freezing. For snow chances in the western and southern Alps, we'll have to look at the weekend, but for now it doesn't seem to bring any serious snow amounts.
At this moment, especially the Eastern Alps are having to deal with a nice cold upper air of up to -10 degrees at 1500 metres. In the Western Alps it's a lot milder with 0 degrees at this altitude, but still these temperatures are not too bad for early March. In the course of the week we will have to deal with rising temperatures with on Thursday and Friday up to 5 degrees at 1500 meters. With values of 15 degrees in the valleys, it will be full spring weather. Due to the clear and calm nights it will remain cold at night with moderate to severe frost in the valleys possible.
The warming up has to do with the displacement of the high pressure core. At the moment, the core is still over England, but in the course of the week it will move further and further east, which means that the cold northeastern winds in the Alps will be over.
The easternmost part of the Alps will continue to experience colder air masses due to a northeasterly flow, but the real cold air masses will be for south-eastern Europe this week. With upper air temperatures of -10 degrees at 1500 metres and towards the end of the week even temporarily -15 degrees, winter will once again strike hard. Especially in Greece, it can bring a substantial amount of snow in the mountains.
On Friday, some cooler air may flow into the Po Valley from the east, which may bring some snow to Piedmont again. There might be 5 to 10 centimetres of snow. During the weekend there might be some precipitation from the west (see the approaching front above in the fronts map), but for now it's only a few centimetres in the Western Alps. The European model did show some interesting amounts yesterday in the Alpes-Maritimes, but by now it looks like these are not the quantities to write home about.