Yes. We've been to France and Italy with a dairy allergy. It was fine, but we were with British based companies (Mark Warner, Esprit, Ski Total, Crystal). We didn't have the milk substitute the first day, but after that it was fine. The chefs made various diary free cakes and the last one in Italy really got into it and made all sorts of creations.
The chefs were all British doing a season though. The largest place we stayed was a chalet hotel, but the others were smaller and so knew the child involved and were very engaged. You might find a large hotel harder. There are often swimming pools in the town if that might add an option
