[NoDOHC]

Ok, please correct me if I am mistaken, but you are talking about a starting issue here.

The alternator only produces current to charge the battery after the engine has started.

You could put the greatest alternator known to man on that car and it wouldn't help your starting at all.

What you need for good winter starting:
A GOOD battery.
Low contact resistance on every connection between your starter and your battery.
Low viscosity motor oil (don't go less than 5-30).

I drove my '86 several winters back when it was stock and it started just fine with many more than 120,000 miles (like 160,000 one winter and 180,000 the next).

I could walk outside right now and start it and it is 3 degrees F right now (of course it has an aftermarket ECU and a rebuilt engine now too).

Here is what I had to do to get it to start on a really cold day (below 0F):
Hop in Car, push clutch down enough to disengage, but not too far (added resistance from throwout bearing).
Crank car until it fired, then give 25% throttle instantly.
Car would sputter a little, then rev to 3,000 rpm.
I could then gently release the gas, keeping the revs at 3,000 rpm.

I was using:
725 CCA battery
5W-30 Motor oil
Stock ECU with 12 degree advanced timing.

Now I have:
550 CCA battery (behind the passengers seat)
15W-50 Motor oil
Haltech ECU

The car starts much better with the Haltech than it ever did stock. I don't think that Mazda calibrated the stock ECU to start at very cold temperatures, it is not a mechanical problem, it is a calibration issue.