The total number of reported cases in the year to February increased from 25 to 40, along with one death - the same as last year.
The largest number happened in Ayrshire - six - with three in Aberdeenshire, two in Moray and two in the Stirling council area.
Both the deaths happened in Fife.
Across the UK, the society said nearly two horses a week were killed on the roads last year.
In all, 87 horses and two people died among 845 incidents.
The society said almost three quarters were caused by vehicles passing horses too closely.
It renewed its plea to drivers to slow down when approaching horses and give them more space when overtaking.
The Dead Slow campaign urges motorists to pass horses at no more than 15mph, not rev their engine or sound their horn, pass with a minimum of a car's width and then drive slowly away.
A spokeswoman said: "Horses have very sensitive hearing and eyesight.
"They are going to damage your car a lot if they kick.
"They are only on roads because there are not enough off-road routes."
The society said one third of riders had suffered road rage or abuse, mainly when a vehicle passed too close to a horse.
Figures since 2010 show 315 horses and 43 people have died in 3,737 incidents, with nearly 2,000 people and horses injured.If I see a horse on the road then I will …
The society lobbied politicians at the Scottish Parliament last month in an event sponsored by Aberdeenshire East SNP MSP Gillian Martin and backed by Police Scotland.
It is also trialling a new app with riding technology firm Huufe to enable people to report incidents more easily.