all electrical equipment goes dead in car. If disconnect battery, then again appears to have electrical power, no fuses in panel or battery relay blown, but ignition clicks once and all electrical out again in car and starter does not engage.
Sounds like the ground cable is loose.
Sure sounds like bad connection at battery or solenoid.
Starter problem it sounds like. Starter solenoid more likely. Take a pry bar of some sort, place it on the starter solenoid if you can reach it, and tap on it while someone else turns the key. If that doesn't work, remove the starter, and replace it.
Try cleaning or replacing the battery terminals.Sometimes the wires get corroded as well. This causes a disconect when a load is applied.
It sounds like you have a bad connection or ground at the 2 battery cables. Or, one of the battery cables themselves is no good. It may be frayed or separated at the end of the cable. Your battery may read that it has enough voltage but if it fails under load then it won't start the car. Have the battery load tested or hook it up to another car and see if it starts it. The cold always makes a battery show when it's at the end of it's life because it makes the battery work harder when it's cold. Another possibility is the late 80's to mid 90's Fords had poorly made ignition switches. It could be your ignition switch. There was a recall across many Ford models including the Mustang. If you have your original switch then that could be the problem.
