Be sure to load jackets. Unlike TX it's still going to be cold in them thar hills. Years ago Yellowstone did not open till after the 6th of June due to snow pack. The Tetons will also probably still be snow capped and beautiful. Enjoy.
X2! We were in Yellowstone TWICE in mid-June (1990 and 1994) and it was snowing both times.
1988 Coleman Sequoia - popup (1987-2007)
2012 Roo19 - hybid (2012-2015)
2016 Mini Lite 2503S - tt (2015 - ???)
2011 Traverse LT, 3.6L, FWD
2009 Silverado Ext Cab, 5.3L, 4x4, 3.73
2016 Silverado 2500HD Dbl Cab, 6.0L 4x4, 4.10