The 2 bad things about the n62 engines are the valve stem seals and the intermediate leveler................check the other post about the Levelers .............how many miles on your x5?

How many miles on her?

Yes expansion tank... I can tell it is coming from the bottom of the tank. See photo

She just broke 83,000 the other day.

I don't see how that is going to effect smoke in your exhaust? Either your valve stem are shot or You CCV has failed...............

Lucky You , You can check a bunch of things but I would.
Check the CCV and clean them
Check the cold start [see if your engine misfires]
How often do You change Your oil? and what kind? [Use Castrol Titanium and change every 4k miles.
On cold start let the engine warm up just a bit[ these engines are all about the oil flow[trust me]
I know this is my second x5 [had the 4.6is] and just make sure the simple things are correct .They are hot running engines, they like to run but when up to temperature.
Good luck.

She has had crazy problems with cold weather engine misfiring. I have read that this is a problem that basically cannot be fixed. I just recently had the thermostat and coolant thermostat replaced and this is when the new problem began to take place.

the misfiring is the intermediate levelers [basically the motor on top of You heads and where they connect to the head cams ] with the low miles You should be okay[for real] check your plugs and replace them[really not hard to do ] .
Good luck.

Of course it won't OP had two problems losing coolant and smoke. The smoke could have been coolant smoke. Now that coolant smoke has been eliminated and it is not black smoke that leaves oil smoke.

Replacing the expansion tank is straightforward with basic tools. Have at it.