In winter, the oil gets milky due to moisture condensing into the oil. So don't get too far into repair yet.
The milky oil usually clears up if the engine is operated for 30 minutes at 30 MPH.
Also, if coolant is getting into the engine, then the exhaust smoke will be white.
SO, first look for an external leak. If you can get a black light (UV) you could add some fluorescent dye to the coolant
and search using the black light. That is what garages do.
If the leak is major then that is a different problem.
scoot safely,