Good question. I know of only one place for sure that is open for summer skiing, Zermatt. Saas-Fee is a possibility but I can't say for sure, especially since their entire lift system is shut down now. Passo Stevelo in Italy is possible. Chamonix in France is possible but you had better hire a guide for that since you would probably be skiing the Vallee Blanche. Austria is the winner hands down with some eight places open for limited summer skiing: Dachstein Gletscher (4 km); Hintertuxer Gletscher (86 km); Kaunertaler Gletscher (36 km); Kitzsteinhorn Gletscher (41 km); Molltaler Gletscher (71 km); Pitztaler Gletscher (68 km); Solden (150 km); and Stubaier Gletscher (110 km). More often than not the number of kilometers is for the winter season so the actual amount open in the summer may be dramatically less. Also, some places are open in pre-autumn seasons only like Solden which is closed for the summer but reopens it's glacier in early September. So, I cannot think of any other places open to ski in the summer in Europe. Go to the relevant website for current conditions and operating times/dates. Good luck.