Yes. ENSO is used as this "Nino or Niña" equation, but it is actually a multi faceted machine that has feedback loops with dozens of other factors that have their own influences, etc.A prediction based only on "is it El Nino or La Nina?" is unlikely to be be useful. A range of other factors influence snow fall.
The forecaster called The Grasshopper on mountainwatch.com is issuing pre-season forecasts for Australia and New Zealand based on a range of factors including ENSO and various ocean temperatures. Then looking at the snow falls for years with similar conditions. There may be much more to it (which may or may not include goat entrails) but since I've been taking notice, those pre-season forecasts (made around April/May) have been a pretty good match with actual.
The Grasshopper clearly reads a lot, but doesn't really understand how to put it together IMO, and puts more of a priority on a nice sounding article. His general medium term forecasts also reflects this.