1965 mustang door and window problems

probably that the latch is in the first lock position preventing it from locking properly
use a round bladed screw driver , place it under the latch and press the door button and the same time pulling the latch out

Sounds like the door switch is not switching or not connected. Sometimes the switch is external in the door jamb/closing area, sometimes it is part of the door catch. Maybe check if the door light on the dash stays on, also if the interior light works on door setting.

My 02 Mustang's light was still on because of the door ajar button. Open the door look at the latch. The latch that goes up and down has a door ajar button hiding near this. It can be hidden by a rubber covering on the side of it. Or you can take the door inner door cover off and try to squirt some oil into the door ajar. You can try oiling it and work it back and forth. Also on the the latches sometimes they dip them in plastic. Mine was loose and would not let the door shut properly. So that was another problem with the light being on. I cut off the pieces that were jamming the latch up.

I would try lube first. Cold weather can cause parts to get stuck.
Normally a door latch will outlast the car, but it could be wearing out.

sometimes when it is this cold after car heats up and gets cold again the door mechanism ie latch can refreeze

door ajar switch in the door latch, they sometime get stuck ,if you try spraying some lube into the latch and open and close the door a couple of time some times they will un-stick otherwise you will need to replace entire latch.

try pulling the door handle a time or two, perhaps the latching mechanism is stuck in the latched position. sometimes pulling the handle and moving the latch with a screwdriver is needed. if this doesn't work then try lifting up on the door while shutting it, if this works then you need new door hinge bushings or new door hinges

wiring connections or lock latch frozen --to manually bypass latch or to unlock rear hatch -- in the bottom of door panel is a round access hole remove cover just clipped into place using a flashlight and a screw driver about 3 inches in on bottom is the lock latch and window lock latch connections if u pull back on the inner latch u will unlock the hatch which will allow u to open it[ when opened check the wiring connections for corrosion or damage if good ] now u can remove the whole hatch panel and check the latches and actuator the actuator and latches,and rod clips sometimes need to be lubed or sometimes the clips break or disconnect clips can be purchased at any auto store panel is clipped into place carefully pry from a corner and using a screw driver or panel tool pry straight back till panel clip pops replacement of panel put clips in place and push in panel

i would try to clean it out by clean it out i mean take it apart and clean it probly got some class in there not shure open door use a screw driver as a door rip see what it deos

this is a very common problem we have seen it many times
you need to replace the outter door handle assembly and then it will work like new.
good luck
paul