It sure reads like your voltage regulator isn't working, i.e. voltage to rotor isn't changing.
With no electrics on, voltage should be stable, as you turn on lights the voltage might drop and then come back up, thats the regulator working.
Yours only seems to drop???
Are all 3 wires coming out of the regulator hooked up
A - (yellow)goes to either B+ on alternator or to Solenoid (Battery side)
S - (gray or white)is a short jumper to single plug on alternator(this wire can get frayed ends, only 1 or 2 strands holding it)
I - (green) goes to Key switch via voltage meter or "charge light" in dash board
(does your dash meter or "light" work, if not that could be the problem)
Also check your digital multimeter, with engine off battery voltage should be 12.6-12.8vDC
If it's showing higher then meter is off.
Cold effects the batteries ability to convert the chemical reaction into amperage when starting, chemical reaction is just slower when colder.
And for the same reason recharging a battery can take a bit longer, when temps are low.
The voltage regulator controls the alternators output by reducing or raising the voltage going to the rotor, that is what the brushes are for, to control the output voltage.
The rotor is an electro-magnet, it spins inside 3 "fields", the 3 fields supply the power to the charging system(B+), spinning magnet = electric power, stronger magnet = more power, so as voltage at the brushes is increased the magnet becomes stronger.
The regulator might supply the rotor 6volts for a basic load, as more electrics in the vehicle are turned on the regulator will increase the rotors voltage to 10volts, stronger magnetic power in the rotor increase the output of the "fields".
So if every thing is working as it should, you should see a stable voltage until you reach the amp limit of the alternator.
So engine warmed up, idle at 700rpm, battery recharged after starting, ALL electrics OFF.
Measure voltage at battery, should be about 14v, 13.8-14.2, now turn on the electrics, you might see a drop then back to 14v.
With everything on you might see a .2 drop, more than that and you are at the amp limit of the alternator.
A charging system can maintain the batteries charge down to about 13.5vDC below that and battery won't be charging and below 13.2vDC battery will be discharging.
From your description all you see is a drop in voltage as things are turned on, so rotor voltage is fixed, the regulator isn't changing it, so it is stuck on 12v, full output.
The chemicals in a battery start to turn to vapor at about 2volts above battery voltage, so if a battery shows 12.6vDC at rest then a charge voltage of 14.6vDC will start the vapor process, the new sealed batteries are better at resisting this, they condense vapor to return to battery.
But prolonged +2volts can take its toll.
And I believe the Ford 3G is a Type A regulator, it uses the rotors Ground brush to control the voltage going to the rotor.
Type B uses the + voltage brush.
Type I uses both brushes, I think chrysler used this.
So with a Ford 3G running a Ground wire from alternator case would be a good idea, just to make sure everything is connected.