Matthew, you've been around this site enough to know the realities of the industry. Golf course architecture is obviously a tough field, but there will also inevitably be golf course architects in the future.
You're also well connected simply by being on this site. As others have mentioned, your ability to gain field experience over the next few years will likely be far more important than your choice of major and school for determining your long term success. I don't want to say that a major is inconsequential, but I'm an English major with a Masters in Education. Naturally, I teach doctors how to manage the care of patient panels and get ready for Obamacare for a living, while also designing electronic systems and workflows for the organizations that employ them.
I couldn't have projected myself in this field, but the skills I learned in school help me do my job every day and far more effectively than a healthcare related degree would have. I would encourage you to think outside the box a bit and figure out specific skills you’ll need to succeed as an architect. Too many people go to college thinking that getting a degree will get them a job in their chosen field. I was one of them. I’ve since figured out that the value of a degree has diminished in the last 50 years as more people have gotten them, but the value of real and tangible skills has gone up because so few people actually have the capacity to effectively apply the things they’ve learned.
Get work experience. Take business classes, assuming you’ll want to open your own firm someday. And I like the engineering degree idea that a few people have offered. It’ll likely be just as valuable as a landscape architecture degree for breaking into golf architecture, but the skills you’ll get with it will also likely apply to more lucrative employers in other fields upon graduation. I don’t like to plan too much for a fallback option, but in the same way that strategic golf holes allow you to choose a difficult path off the tee to gain an easier second shot, college offers you the opportunity to really challenge yourself (in terms of academics and also finding valuable field experience) for four or five years to gain an easier post-graduation lifestyle. In golf, it sometimes makes sense to avoid the risk off the tee and just face a tough angle on the second, but in life, I’d rather take the tough path while I’m in my early 20s and have an angle over my peers afterwards. When in doubt, go with the tougher curriculum that offers a higher salary upon completion.