On the contrary: January so far has been significantly sunnier and warmer than the long-term average, especially at the mountain stations. There were always warm days in the valleys when the cold air was cleared out by freshening winds - in the north typically light Föhn winds with a SW flow. Otherwise, it will continue to shiver in the tough inversion.
Outlook
The whole thing will continue unchanged until Friday: zonal flow, frontal zone far to the north, high pressure influence in the Alpine region. If it's boring long enough, you're happy about the smaller changes, so now the more or less exciting message of this WeatherBlog: It's going to be cloudy on Saturday! It's even snowing a little in the north! We have a cold front to thank for this, which will slowly become active in the western Alps on Friday afternoon and then move on to the eastern Alps in the night to Saturday. As far as the amounts are concerned, the WeatherBlog is not particularly confident that it will be enough for a report from colleague Orakel (the threshold for this is known to be 30cm), but maybe we'll all be surprised. In any case, it's likely to get colder, although that's not too much of a stretch given the current situation in January.