THE DREAM OF owning a winery is one that many may harbor but few are actually able to fulfill. The expense is considerable and the odds of success are incredibly long. Yet the list of actors and athletes, financiers and film directors who aspire to see their name on a label simply goes on and on.

After a recession-related pause, the number of would-be vintners has been growing of late, according to real-estate brokers who specialize in the market. And some recent high-profile sales, such as the purchase of cult-Cabernet...