I am planning to go to St Moritz during first week of June. I u derstand that this is a shoulder period. What's the weather like at this time of the year? Am also wondering what kimd of footwear I should bring. I will be heading down to Lugano, Milan, Paris and Belgium after St Moritz, so for those legs I plan to be on sandals and running shoes. For St Moritz, would a pair of trekking shoes be necessary? Or wellies?