That picture is of Teton Pass, elevation 8431 ft. The valley floor (Jackson Hole) is about 6200-6800ft. It's unseasonal, but not rare, to have a snow storm. When I lived there, my family came to visit once over July 4 holiday. We went to Yellowstone, even higher. It snowed. The roads were not slick, but snow was on the ground and stuck to all the trees, everything was white. I was told Teton Pass had 12 inches of wet snow that day. After the weather cleared, back in Jackson, we went to sit outside and watch the fireworks that night. The temperature was in the upper 20's. I had to loan all my family warm coats! Old-timers used to brag that it could snow any month of the year, and had.

To be fair, though, it can get quite warm in the daytime (if the sun is shining) and then drop 50 degrees after dark, due to the elevation.
WYZ012-112200-
/O.COR.KRIW.SN.Y.0043.080611T1335Z-080612T1200Z/
TETON AND GROS VENTRE MOUNTAINS-
735 AM MDT WED JUN 11 2008
...SNOW ADVISORY IN EFFECT UNTIL 6 AM MDT THURSDAY...
THE NATIONAL WEATHER SERVICE IN RIVERTON HAS ISSUED A SNOW
ADVISORY...WHICH IS IN EFFECT UNTIL 6 AM MDT THURSDAY.
A PERIOD OF STEADY SNOWFALL WILL BECOME ESTABLISHED DURING THE
MORNING HOURS TODAY. THE SNOW WILL BE HEAVY AT TIMES THROUGH
TONIGHT. ELEVATIONS ABOVE 8000 FEET SHOULD SEE A SNOW TOTAL OF 4
TO 8 INCHES BY SUNRISE THURSDAY. ROADS ABOVE 8000 FEET INCLUDING
TETON PASS ARE EXPECTED TO BECOME SLICK AND SNOW
PACKED...ESPECIALLY BEFORE 9 AM THIS MORNING AND AFTER 9 PM
TONIGHT.