At about mid summer in 2003 - the hottest summer ever recorded until then - we saw substantial quantities of snow on north facing slopes in Yosemite at around 3200 metres altitude. This was at the location shown by the + in the middle of this map looking South East across Ellery Lake.
As that was substantially lower than your 3900 metres, on a probably hotter year and close to midsummer, you'd be wise to allow for snow as a distinct possibility, but not a certainty.
In late June 2003, the then hottest year on record, we travelled by car from Mono Lake into Yosemite. The road rises to around 9600 feet at the highest point at Ellery lake, and the road then remains at about that level for some miles.
There was no snow immediately near the the road anywhere but when we got to Ellery Lake there were substantial amounts of snow on the slopes on the far side of the lake. These are more shadowed north side slopes rising to about 11,000 feet.
Your 3,900 metre road is at 12,800 feet (!) which is well above the level we saw snow at. Further into the park from Ellery lake the top map says "Closed winter" but the altitude is about the same as at Ellery Lake.
Location map here - viewpoint and direction of view about right. Snow may hav ebeen somewhat higher up slope than shown. Photos available.