Odds of Getting In
Landscape design is one of the few horticultural industries that really appreciates formal education. When jobs are available, those with some sort of degree in landscape design or a related field are far more desirable than those without.
Larger landscape firms that design landscapes for the sort of new development that's always being developed hire new landscape designers on a relatively regular basis. (Even landscape designers eventually retire.) These larger firms are more selective than their smaller counterparts, though, and prefer those who did well in school and maybe have a bit of experience. Smaller firms are a little less picky, but they also rarely promise such reliable employment as what the big firms offer.