November and December (watch out santa!) are the most dangerous months, and in the north of Finland.
More information here from Sikunews:
"The most dangerous stretches of road are between Pudasjärvi and Kuusamo, as well as on Highway 5, north of Kuusamo.
Around 3,500 to 4,500 collisions with reindeer are registered annually in the north of the country, and about 40 per cent of all collisions with reindeer happen during November and December.
In general, defensive driving is the best guarantee of traffic safety and for avoiding reindeer on roads." about 8 years ago
Just to add to Phil's answer - you only get reindeer on the roads in Lapland and in general in the more remote areas.
You do get them on the roads in the summer as well as the herds are crossing from one side of the road to the other, but I guess the fact that the roads are covered in snow/ ice and that it's dark in the winter makes a big difference to the accident statistics.
More serious ones accidents are caused by elks and they can be found all over the countryside, both in the south and north. Winter again being the time when a higher number of accidents occur but from memory it starts to be more dangerous in terms of elks darting on to the road in the autumn/ winter when it's darker.... about 8 years ago