If a car stops running due to low oil pressure, the engine is usually fucked at that point. So the short answer is if it restarted, I doubt low oil pressure is your issue.

It sounds like in extreme cold, you're running into gaskets failing and causing a vacuum leak. Which would cause the engine to die.

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2011 M3
2006 Sierra 2500HD 4WD LBZ/Allison
2004 X5 3.0i 6MT
1995 M3 S50B32
1990 325is
1989 M3 S54B32

Hers:
1989 325iX
1996 911 Turbo