The weather at Cortina d' Ampezzo is very unpredictable, mainly because it is surrounded by the Dolomite mountains on all sides, which tend to trap rain clouds especially during summer. When I was there during June 2007, the weather changed from good to rainy very quickly, then the rain stopped and started again and again. Also, the mountains disappeared into the clouds and then re-appeared again and again. Be prepared for the weather here.
Although September is a warm and often sunny month it is the time when Cortina closes down. Apart from Lagazuoi all the cable cars are closed as are the majority of rifugios up in the hills and many of the hotels in the town. The winter season is the big money maker and the locals are either geting ready for that or taking a well earned break after the summer. To be fair the snow is not long in coming and there can be snow at Cinque Torri in September let alone the higher points which the cable cars give access to. The local bus service is not brilliant in the summer but that too closes down in September so you are left with your own legs or taxis to get up the hills.