Odds of Getting In
Like so many other horticultural industries, wholesale nurseries have a problem with ethnic discrimination. Larger wholesale nurseries that do more growing and less marketing have more of a problem with this than smaller growers and wholesale nurseries who sell directly to landscape professionals (instead of simply selling to other outlets where landscape professionals or retail customers shop), but on the whole, it's something to be aware of.
This is also a fairly competitive business to get into. It helps to have experience and some education - at least a high school diploma,a and maybe more. You may need to take another job while you wait for the right nursery job to become available. Or, if you want to be more proactive about it, you can sign up on NurseryMatch.com, fill out your profile, and hope one "winks" at you.