I took the tour in early June. Everyone was in summer clothes most of the time, maybe a light sweater or jacket some evenings. The day hiking in the Alpi di Siusi started out fairly cold (you'll be on an open T-bar lift to the hiking trails) but after a couple hours we were all shedding layers. Then mid-afternoon it turned chilly and very rainy for a couple hours, so the layers went back on. For the mountain tops (Zugspitz, Lauterbrunnen, Chamonix) I was glad to have a thermal layer under my fleece jacket (windproof would have been much better), and winter hat, gloves and scarf. But you're only up top for an hour or two each time and there are indoor places to warm up. At least as important is taking enough water and drinking a lot to avoid or limit altitude sickness, UV-protective sunglasses and sunscreen.