As the proud owner of more the $1700 worth of digital meters I say it is total folly to say the analog meter is better. Yes the cheap digital meters will have display settling issues but to say you can't measure a static resistance accurately with one is just ludicrous.
There are only two places where an analog meter is superior. One is for peaking or nulling as the action of the indicator needle is fast and relative. The other place where an old analog VOM is superior is for measuring circuits where you need a little loading to pull down stray voltage, old analog meters don't have high input impedance. Of course this will cause inaccuracy when measuring a voltage on a high source impedance... You could always shunt the input of a DMM with a 100K resistor to make it mimic an old VOM if needed.
If the refergeriator runs fine, there is just no need to measure the winding resistances. Generally the only reason they would change would be due to an open or short and then the motor will no longer run. You could measure resistance to the chassis to test insulation integrity, but then you will need a GOOD digital meter since that will be many Megohms.