As someone who is currently in an undergraduate landscape architecture program and shares a similar passion for golf courses, I'd probably tend to steer you away from that path. I think Jeff is right in that most of what I've done in design studios the past couple of years would offer you little in the way of an education in golf design. For example, right now I am working on a park design/greenway, examining the world's water crisis, as well as drawing construction details for walls, ramps, steps, pavements.
I think what landscape architecture has offered me is as someone trying to also make a go of it in the golf design/construction field:
1) learning design process and site analysis
2) learning what is called, "design implementation" in school -- grading, stormwater, planting, materials and construction all of which have taught me some things, but mostly reinforce or contradict what I've seen in the field working.
3) learning computer programs and a few hand graphics
But I think I've learned far more from laying down sod, staking greens, digging drainage, finish shaping bunkers and greens, and hanging around an office than in the landscape architecture curriculum. And I think getting those opportunities has had more to do with the fact that I've been eager, lucky, and had previous experience than that I am in a landscape architecture program. If you're really set on getting back to school I'd probably tell you to find your way to a turf program as its a better "in" to the golf world, would take less time, and have a greater golf focus.