The Alpine winter in Chamonix brings us ice-climbing with reasonable access. The days will be full on mountain days, but they finish with hotel nights. You return to hot showers and beers.
Chamonix has very good ice climbs, some areas such as the right bank of the Argentière glacier are world class with classics such as Grand Blue, grade 4+ and Shivaling, grade 6, while the left bank has the easy-to-access classics Nuit Blanche, grade 6, and Déferlante, grade 4.
Not far from Chamonix are a host of reliable ice climbing venues. A favourite area is the Cogne valley, a world class ice climbing spot. Although there are some very hard mixed climbs (example: the X Files one of the first M10s, climbed in 1997 by the eccentric Stevie Haston) there are also an abundance of climbs ranging from the easy (Lilaz Cascade, grade 3, is arguably the the best climb of its grade in the Alps) all the way up. One that is worth mentioning is Lau Bij, grade 5, which finds a reasonable route through overhangs of icicles, producing a wonderfully airy situation with overhangs above your axes and a void below your crampons, all at a surprisingly reasonable technical level.
If conditions are good it may also be possible to go to Switzerland instead of Italy.