In that case you might try driving along the south side of the lake toward Evian-les-Bains (a couple of rustic hotels on the lakeside with good food), and turn south at Thenon-les-Bains and head into the mountains.
I’ve only been in the summer, but there are lovely little towns on the way to Morzine – which is a ski area, but not developed in the way Chamonix is.
You can do pretty much the same from Turin, heading toward Susa, then up over the mountains back into France, where you are in the middle of a national park.
But the Turin airport is often fog-bound and GVA operates well, even with snow.
Total distance in each case is only 50 – 60 km.