Which peaks in the Alps would make reasonable moderate ascents around Christmas time?

By moderate, I mean no technical gear other than basic glacier gear (rope, ice axe, crampons, etc.). I want to take the wife and kids so can't do anything really difficult. I wouldn't want anything with extreme avalanche danger either.

(We are thinking of 2017). I can't get time off in summer and the kids are in school in winter, except for the Christmas holidays.

Maybe something like Mont Buet? Any other suggestions?

Pity that you can only come around Christmas. It's one of the busiest times in the Alps, because many people are on holiday (schools are closed all over Europe). That said, the vast majority of those that come to the Alps in winter do so for skiing, and relatively few will venture off piste.

The good news is that there must be thousands of reasonable moderate ascents that you can still do around that time. Of course, the daylight period is relatively short, so that's a limiting factor. Also, almost no mountain refuges are open for business unless they are by the side of the piste, so, considering you're with the family, I reckon you're looking for day trips.

With all that in mind, I'm thinking about the area south of Innsbruck. You can choose from the Stubaier Alps, Ötztal Alps, Tuxer Alps or Zillertaler Alps, to name a few. Staying in the Austrian Alps is a little bit cheaper than in the French Alps, and a whole lot cheaper than Switzerland. You can stay in a ski resort or avoid the pistes altogether. Depending on the weather and the avalanche conditions at the time (impossible to predict far in advance) you can ski on the prepared slopes or off piste, climb frozen waterfalls (though Christmas is a bit early) or go snow shoeing. If it's glaciers you like, the southern parts, near the Italian border are the best.

Another good option is the area just south of the Austrian-Italian boder, which is the Italian province of Alto Adige / Süd-Tirol. Prices are comparable to Austria, and as in Austria, you can choose between all sorts of activities.

I find it difficult to give suggestions for any particular peak. First of all, I don't know how long a route you're looking for. Also, on skis you'll be able to do a fast descent, so you can do longer routes than on snow shoes in the same amount of time. And, as I wrote above, what's feasible will depend on the actual weather and avalanche situation by Christmas.

That said, assuming suitable conditions, an example of a ski ascent you might consider is the (Wildspitze (it's in German; you can use Google Translate to get the idea)). SP has a succinct route page. It's a glacier tour, but not overly long. On a clear and sunny day, the views should be fantastic.

Also, almost no mountain refuges are open for business unless they are by the side of the piste, so, considering you're with the family, I reckon you're looking for day trips.

Multi day trips are fine. We're used to sleeping in -30C temperatures anyway.