This happened gradually, or suddenly? That is pretty severe oil loss...generally, that is a CCV issue. If something is clogged or not draining properly, all of the oil is pulled from the valve cover into the intake by the vacuum (ahem, absolute pressure lower than atmospheric to make the forum happy) of the engine.
Afaik, oil only gets into the combustion chamber via the CCV system, piston rings, or valve stem seals. No external engine oil leak is going to come out the exhaust, and 2qts in 350 miles is going to fill the belly pan and leave a huge puddle sooner rather than later. You're burning, not leaking.
After moving to NoVA...TN winter is nothing, and I'm sure this is only the tip of the iceberg. I hear the weather there is nice right now, be glad it isn't 50 like it is here!