. . . by leaving the key in the ignition in the On/Acc position from Sunday night until Tuesday morning, on Tuesday morning there wasn't enough juice to light up the interior light, like totally dead. I jumped it and ran it for my 50 mile round trip to work and back and the battery now reads at 12.40V and the green Hydrometer is faintly green.

My question is, should I charge the battery using a charger or will I be good with letting the alternator charge it? If the battery was totally discharged for maybe 12-24 hours total, will that be bad in the long run. I do know that a battery left with no charge will be rendered useless in a short time, but as it was not discharged for long will there be any long-term damage?

I worry because here in New England we have some coooold mornings and when we leave our trucks for 2 day weekends I have to trust that my truck will start in the -20, -10 degree nights/days up in the top of NH.

 

I would use the battery charger if you've got one. Charging dead batteries with the alternator is a good way to overheat and kill your alternator. Alternators aren't designed to charge totally discharged batteries, just to keep them topped up.