With cloud and cold air stuck overhead, Nome has seen the coldest first 10 days of June since 2006. Another statistic: the week ending June 8 was the third coldest week entirely within June since 1977; but 2006 and 2013 both had slightly colder weeks in early June. Like this year, 2006 and 2013 both had major disruptions to the stratospheric vortex in January; there may or may not be a connection (perhaps more likely not), but I'm always on the lookout for these things.
Some fresh snow has been seen at various locations around the Seward Peninsula: here's a photo from Shishmaref on Tuesday (June 8), courtesy of Alaska DOT&PF on Twitter.
And here's a video of snow in Nome on June 5.
As for the larger context of Nome's temperatures so far this year: it was a chilly end to winter, but spring has been considerably warmer than normal most of the time since mid-April.