When the weather gets colder the effective power in a battery goes down dramatically, but the starter takes more power to turn and the engine takes more out of the starting system because of greater drag due to cold oil, etc. So, what is a marginal starting situation at milder temperatures becomes an impossibility at colder temperatures.
If the headlights do not dim at all then usually the solenoid has not "clicked" indicating that the pinion gear has not been moved into mesh with the flywheel so that the heavy contacts in the solenoid can make contact with the heavy starter connections to turn the engine. Or the solenoid does "click", but the heavy contacts are burned and not allowing sufficient power through to turn the engine.
I would begin by removing the battery connections and cleaning them, but not re-attaching just yet. With the battery disconnected clean the pos battery connection to the starter solenoid on the starter and clean the small wire connection from the starter switch to the solenoid. Check any exterior connections from the solenoid to the starter since they may be causing your problem. Clean the neg cable attachment to the engine ground which is often the starter mounting bolt.
Check the voltage of the battery, but this can vary, 12.6 is fully charged. A better home test is the specific gravity of the electrolyte in the 6 battery cells. Remove the caps from top of battery and insert a battery hydrometer ($3 tool is fine) feed tube into the cell and draw up the fluid and expell a few times to even out any stratification and when the tester is completely full of electrolyte (sulphuric acid) read the specific gravity with the unit upright. A reading of 1.3 is very good, 1.275 is good but lower than 1.25 is poor and the battery needs to be charged. Repeat for all 6 cells. They need to be uniform, and if one is way low compared to the others then the battery is likely no more good.
Re-connect the battery using die-electric silicone grease on the posts and the cable ends. Tighten the battery connections. The grease will not impair the electrical contact but will seal the connection against corrosion. Clean the battery top and ensure the plastic cover over the battery fits properly. This cover protects the electrical circuits close to the battery from corrosion.
If the battery still has a problem turning the engine over, check that the starter solenoid connection (small wire) has power. It comes from the neutral safety switch (now called Transmission Range Selector TRS) and could be damaged or poor circuit. If this is OK then you need a battery load test at a shop and a starter load test at a shop to confirm which or both to replace. Try Autozone, Pep Boys or Checker to see if they are still offering free tests.
Hope this helps.
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Art
2000 Taurus SEL Wagon 3.0 Vulcan (daily driver)
1993 Taurus GL Wagon 3.8 Essex
1991 Mercury Grand Marquis LS 5.0
1986 Chevrolet 3/4 ton pickup 4x4 350 with turbo400 and 208 transfer case
1978 Chevrolet 3/4 ton pickup 4x4 custom 6.2 na diesel with turbo400 and 203 transfer case
Planning 2008 Taurus X in a year
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