Dexron III is a specification for ATF oil
I recommend you these oils:
for Diff: Castrol SAF-XO or SAF-XJ (for classic diffs - no LSD)
- specs: 75W90 or 75W140 - SAF-XO or SAF-XJ meets all these requirements.
for engine: M20 engines (little six) - 15W40 oil or 10W40. (15W40 is recommended by BMW for M20s
M40 and M42 engines: (318i or 318is, also E36 318i etc.) - 10W40 or 10W60 (for racing M42s)
Tranny: Dexron III spec. ATF fluid or 75W90 common transmission oil.
Beware - the ATF fluid is very washy, so an old and worn tranny will be noisy. But gearchange will be easy in winter, though...