May and June are two different animals - I really can't see why one would compare conditions in May to conditions in June. A whole bunch of snow will melt of between the middle to end of May and the middle of June.
Every year is different and there is still plenty of snow out there right now due to late season storms, but this was not a big snow year. You have a good chance of not needing any winter gear in the middle of June this year.
