Cointreau?! I shudder at the very thought. There is exactly one authentic recipe:

Reindeer Tear (Poronkyynel)

Ingredients Instructions
  1. Drop cranberry in vodka.
  2. Drink.
Most Finns are familiar with this drink, but as you can probably figure out, it's a joke, son. The cranberry has a hard waxy skin, so when dropped into a glass of vodka it just sits there, a shiny red ball in a glass of transparent liquid, perhaps looking vaguely annoyed but in no way affecting the taste of the drink.

When you actually do drink the shot, the cranberry usually decides to stick to the bottom of the glass, meaning that you have to fish it out with your fingers in a most undignified manner. Finns will not stoop to this and will instead just pour in more vodka, which will either dislodge the recalcitrant berry, or after enough refills cause the drinker to cease caring.

I don't think I've ever seen reindeer tears outside the menus of touristy Lappish restaurants (cf. Aurora in Roppongi, Tokyo, of all places), and undoubtedly it was invented by one of them. But it's certainly a far more authentic expression of refined Finnish cuisine than anything involving sickly sweet orange sap -- for the culinary equivalent, you may wish to consult reindeer hash.