It was the worst snow season since 89 or some shit. Regardless the alps have places where it snows year round, and that have snow cover year round. There's an entire province in Switzerland that has snow covered mountains even deep into the summer.
Ramsau is really close to Kaprun but I think it will be closed by July. You could try Sölden which is not too far and should be open and has a reasonable park. Hintertux (Mayrhofen) would be a good choice but I think it's pretty far away then.