It might happen because of a faulty starter gasket.
Does the engine crank over?
Could be, (assuming the starter is not cranking the engine) a bad starter, dirty or loose battery connections, the engine is seized.
When a engine is real cold, The oil in it becomes thick and heavy, The intire engine contracks and everything inside of it gets tighter then it would be if is was warm. So in terms; The starter has to be in good working condition to be able to turn the engine over. There's alot of starter problems in the winter time.
why would my starter wire burn, going from starter to battery
I would check the starter solenoid before I investigated the starter - it's likely the cause. Have someone try starting the car hot while you measure the voltage between the starter side of the solenoid and negative - you should get battery voltage. If not, the problem is the solenoid (or somewhere before it, electrically).
Weak battery? Loose or corroded battery cables? Starter solenoid?
The starter is burning.
Well if everything but the starter engages when you turn the key the starter is bad, if not then your ignition switch may be bad. Starter would be my first choice in any case.
No. A bad starter would cause the car not to start.
no gas entering piston chambers or no spark in the spark plugs. I assume the starter is spinning the engine?
Dead battery, bad starter, or defective ignition switch.
Misalignment? Defective starter drive? Seized engine? Defective starter solenoid? Burnt out starter?