Glencoe Mountain and Nevis Range snowsports centres have been among places to report having coverings of snow.
A picture by Mark Trigg for his Facebook page Back Corries shows a thick covering on Aonach Mor.
The picture has been shared on Twitter by Iain Cameron, who studies and writes about snow, and Lomond Mountain Rescue Team.
In a message below the photograph, Mr Cameron said: "This is 1pm on Tuesday the 2nd of June on Aonach Mor and this is just ridiculous. Unprecedented, perhaps."
The rescue team has also asked if anyone can remember a longer winter season.
BBC Weather has been reporting how 40 years ago there were snow falls across the UK.
Forecasts suggest temperatures should rise later this week.
Snow has been falling over upland areas of Scotland.