Hi Charlie, my name is Kenny
Charlie first off I think your battery is no good, part of one of my test for checking the battery is, first give the battery a proper charge and measure the voltage as you did, then with meter still hooked up to the battery, turn the key on, then third test with meter still hooked up attempt to start the machine.
So in your case your baseline voltage is 12.5-12.8
Key on you should get about a .5 at the most drop
Last when attempting to start usually 10.0-11.0 VDC while starting
With a voltage of almost 10 VDC with just turning on the battery tells me the battery is no good.
Now I also think that you blew your main fuse, the main fuse is located on the starter solenoid, follow the positive lead from the battery to the starter solenoid, on the solenoid you'll find a 30 amp fuse, I believe you blew that fuse and that is likely from trying to start it with a defective battery. So a marginal battery when transporting from being jarred can internally short, also a battery that is on its way out, yes will be effective by the cold.
Also after getting a new battery, check all the main battery wires to make sure that the mounting points are clean and tight on both ends including the ground wire to the engine !
Let me know of this helps or you have any further questions.