Fraternity work never ends, even over the summer. Especially for exec member, there's always something you can be doing. At the moment, our chapter is in full recruitment mode, hosting events and contacting PNMs (Potential New Members). In fact, I can bet that every other fraternity around the country is doing the same thing.
It's the other things that you normally don't think about that you could be working on. For instance, our exec is going to be starting an examination of our chapter's bylaws next week. Most people don't even think about that. If you don't update your bylaws regularly, and actually read through them to make sure that everything is still relevant, you can end up with rules that no longer help.
Other things to do: party planning and risk management planning. It's never too early to plan out your parties for the semester. Themes, times, locations, the earlier you have all these things in mind, the earlier you can get money ready and get the word out. Think, if you have people talking about your first 3 parties 3 weeks before you even get back in class, you have a HUGE leg up on the fraternities that wait to plan until they get back to school. Now with risk management, there's always something that we do as fraternity men, that is risky or dangerous. Some could even result in our chapter or general fraternity getting sued. And trust me, getting sued sucks for everyone. Even if the general fraternity settles out of court, all the chapters around the country are stuck paying off the bill for years to come. Hense risk management planning. If you can mitigate the risks as much as possible, there's less that can go wrong and less that you can get sued for.
So, moral of the story, it may be summer, but if you're in a fraternity, be prepared to work. It is the summer, so take it easy, relax and be with family (if that's what you want to do). But if you get a call asking you to do something for your fraternity (or sorority actually), don't complain, just help out. Because trust me, the exec has enough work to do already.