Driving in Scandinavia (including Finland for the purposes of this writeup) is not quite like driving elsewhere, especially in the more remote areas. There follows a generalized list of points to look out for, which may or may not apply to particular countries; but rules are generally pretty common across the board.
Dipped headlights should be used at all times, even in broad daylight. (Ever wondered why Volvos have their lights stuck on?)
Elk and Reindeer are liable to jump in front of your car at any time. Common areas where this happens are fenced, so look out especially for the gaps in the fences. Hitting an adult Elk will cause serious damage to both your car, and the elk. If you have to swerve, aim BEHIND the animal; they will stop or run forwards, but won't run backwards.
Speed limits are low. Check and comply with them. For example, towing an unbraked trailer, you are limited to around 30mph.
Distances can be huge. Ensure you know the scale of your map before planning routes. Combined with the low speed limits, it can take a very long time to get places.
Fuel is available everywhere, but again distances can be large between filling stations. Always completely fill your tank at every opportunity. Many fuel stations are automated, but do not be tempted to use the red pump. It contains subsidised fuel for agriculture, and will also dye your tank. If you are caught with a dyed tank you will be fined heavily.
Alcohol limits and penalties are much higher than in many places. Don't drink and drive.
Winter tyres should be used between November and April.
Keep all your vehicle and insurance documents with you at all times.
If another driver wishes to pass you, they will flash their lights, or sound their horn. If the route ahead looks clear to you, signal right and make it easy for them to pass. On multi-lane roads, passing on the right is legal. You may encounter three-lane roads, where the centre lane is for either side's use when overtaking.
Parking lights must be used when parking in a dimly-lit public place.
I am not a lawyer, and this is not an exhaustive list; just points to bear in mind.
Thanks to catchpole for information.