I think that Russian Line infantry during the Seven Years War typically wore green jackets. That is probably the reason.

BTW, I think they often took the jackets off to fight, exposing red vests.

This is the case in the Napoleonic period as well, where Russia is often assigned the colour green (cf. Napoleonic Wars, etc.)

As a (50%) Dutch person, the reason is actually a bit less clear than that: back in the day, orange dyes were much redder than the orange used today on, say, the NYC flag, and moreover faded to look a lot like a red too, so there was always a bit of confusion about the flag. (Insert bit about the sea here, if you like.)

Then, during the Napoleonic period the Batavian Republic, and later the kingdom as ruled by Louis Bonaparte very deliberately chose red as the colour of that stripe to avoid annoying the French. When the house of Oranje was restored, the orange stripes came back, and until 1937 were co-equal with red ones, when the Queen stepped in and specified colours for the flag to head off the fascists.

As a 100% Dutchie, I did not know all that. Thanks for the info!

I know that the colour of their uniform was white but I'm not sure if this is a chick before the egg thing.

Dunno, but they are white in Empires in Arms and (as Austria-Hungary) Great War In Europe: Deluxe Edition too, to name just a couple...

Just as the British were nicknamed "the Redcoats" in believe the Austrians were nicknamed "the Whitecoats" because of the uniforms.

In games covering the 18th century or the napoleonics, Austria is usually white because of their uniforms, indeed.

Similarly, the napoleonic French (but not the French before Napoleon!!) are blue, the Prussians are blue, the british are red, and the Russians are green ...

In Diplomacy they are Austria-Hungary but they are red and Russia is white.

Or Grey, probably because that was the color of German uniforms.

It's probably too much of a stretch to link this to the Brunswickers rather snazzy black uniforms in the Napoleonic wars isn't it?