The latch/lock on back door of Mitsubishi Montero SR doesn't work

Open the rear tailgate from the inside. Now open the door to the toolkit that is usually mounted on the tailgate/rear door. Using a large Phillips screw driver[usually a #3 tip], take the tool kit off the door panel by unscrewing/removing the screws holding it to the door itself. Once you have removed the tool kit, use a knife to carefully cut a "U" shaped access flap in the clear plastic sheet that should have been behind your tool kit. This sheet is called a water shedder or water curtain, it keeps water off the back of any door panel trim to prolong its life. You want to cut that U shaped hole in the sheet where the door sheet metal already has a hole from the factory. This will allow you to peek up inside your door and see how much of the rear door handle broke on you.
You should be able to easily see the guts of the rear latch and the release handle from this vantage point. Try to move the handle on the outside of the door. If any linkage or plastic 'arms' broken during your winter, you'll probably see this as well. Hopefully new parts are available, otherwise, you'll need to access a used Montero in a salvage yard to get good working parts as a repair. While you're in the door, lube ALL latch, cable, handle parts with a light oil to help prevent this from happen[the oil or a light grease will help displace any future water or ice from sticking to any latch parts]
You can easily tape the U shaped cover you made of the plastic sheeting back up into place with some decent tape, like Duct tape or packing tape. Masking Tape will work, but falls apart in a car with age. Clear plastic Packing tape works well and is transparent to boot. Good Luck with the door.