I interned for a relatively well known designer a few years ago, and I will tell you, quite simply, that the summer could have been better spent. He was moving offices at the time, and I spent hours filing and re-filing reports, plans, and other project related documents from nearly his entire career. I also had the opportunity to construct desks and cabinets, and to move furniture (please note the sarcasm).
To be fair, he did take me on a handful of site visits, was usually willing to call ahead to courses that he had built and arrange a tee-time, and had an extensive library which was available to me to read through at any time, and simply looking at the old documents was intriguing. He actually had hand-drawn contour maps for green complexes he had designed earlier in his career!!
What it comes down to, though, is time. Few are going to be able to gain trust in during a 3-month internship, so it's a rarity that anyone will do more than be able to listen in on a few meetings, or do some CAD work or Photoshop rendering.
My advice to future interns, then, would be to make yourself available for a minimum of six (6) months, if not a year, if you plan to get any real sense of what it is like to design a golf course. Or, as stated earlier, you might be better off actually seeing a course built by working in construction. I hate saying that, since it's not what I wanted to hear at the time, but my construction experience was invaluable.