Assuming you don't want to follow convention and get an aircooled three wheeler;

You need to change all the fluids so they'll work at well below the minimum temp, but I'm not sure what to. The F650 has a couple of problems compared to say a Ural. As the clutch is wet you'll need motorcycle oil, no chance to drop in what the locals use in their Lada's as it'll wreck the clutch. Normal multigrades (5W50 if you can get it?) should work down to about -40 so they are getting a bit thick at -20 but won't actually freeze. You'll need to talk to BMW about the antifreeze, there'll be a limit on what strength they'll allow and they may want to change the fill quantity to avoid the reservoir spliting (which I assume is plastic and will go brittle?). The clutch stirring the sump sludge is going to be a big draw on the battery,but again the solo bike can't be fitted with a car battery, the normal solution. I'd fit the biggest capacity gel battery you can lay your hands on and carry a plug in charger too. Anywhere to fit a second battery? Make sure every electrical connection is waterproof, especially anything to do with the FI and starter. If the weather gets bad you are going to have to find somewhere at least indoors for the bike. I'd consider carrying something like a greenhouse heater and a cover to keep the battery and sump above freezing if the only choice is a sheltered bit of carpark. QD connections on the battery are useful so you can bring it indoors.

Tyres wise, narrow knobblies are about the best thing on snow, you can get Heidenaus that are M&S compound. You need to be very smooth and allow a lot of time to do anything, think sand. On ice nothing short of studded tyres works well enough to cover anysort of distance. Not sure how the authorities will react to you using studs on the streets and with the solo bike you can't easily carry two sets. Chains work for short periods but won't survive a transcontinental journey. Chains are useful when you've ridden on cleared roads and meet a bit of snow or ice, but they take ages to get on/off. I assume you'll have a refit planned somewhere along this route? Studded tyres don't last long are aren't nice on tarmac.

You also need to really consider your survival needs. At minus 20 with a heated jacket and ski/expedition gear (no armour, it's harder to fall off three wheels) on an outfit I can ride for maybe a couple of hours before I want to get indoors, I've done 4 but it was getting rough and honestly dangerous. If you touch something like the fuel tank without gloves on you'll soon have frost bite. To change a puncture in these conditions you don't have long and need to work in gloves. There is a point where you have to give up and go get warm, fine if you can hop a mates outfit and plug your jacket in, not so great if you are planning a *****y long walk.

Are you sure about those temps? Minus 20 isn't the maximum daytime temp? Central Russia in winter might see an average in the minus-teens at midday but the low can be minus 40.

I really can't see the F650 solo as a sensible option in conditions in Scandanavia in winter. Russia is going to be worse, so I'm suggesting you think about buying a Ural when you land.

Andy