The explanation is the viscosity of your transmission oil becomes that
of cold molasses at these temperatures, and you can get it into gear
when cold if you are patient.  Once warmed up, it will work as normal.

If you don't want this problem, put some kind of heater under your
transmission.  See  your dealer or auto parts store.

Lg

I would look for a build-up of grease on the transmission shift levers,
which will trap dirt which in turn will absorb water which will freeze.
Clean everything and lubricate with light oil. You can see these under the
hood.

I had one of those beasts for a while in the early 1990s, and if I recall
correctly the end of the cables had rubber boots over them, which could
easily trap dirt.

The advice you received regarding shift cable binding is worth checking
out.  (Especially the cable that selects the different shift forks left
to right)

An extra thought:  I have overhauled 5 or 10 of the K car transaxles (I
think New Process 535s) and during the late 80's it seems like Chrysler
retroactively began specifying ATF for trans lube verses 90 weight.  I
have always used ATF with no problem.  It gets down near 0 degrees F.
here for a couple weeks a year, but shifting my and my customer's
Chryslers was no problem due to the thinner oil.  No durability
problems to note either.

I got a customer in once with a 89 Omni that had a wasted mainshaft and
diff bearings.  It had recently been to a 'Trans' shop who used 90
weight during an overhaul.  The fix was to do it all over again with
new parts and ofcourse use ATF.

Toyota MDT in MO

One cable is for front and back,
the other cable is for left and right.
That one is freezing.
How to fix, I have no idea.
Maybe thaw and lube well.

in olive oil.
Place the meatballs in the tomato gravy, and simmer for several hours.
Serve on spaghetti.
Accompany with green salad, garlic bread and red wine.

Newborn Parmesan

This classic Sicilian cuisine can easily be turned into Eggplant Parmesan
If you are planning a vegetarian meal. Or you could just as well use veal -
after all, you have to be careful - Sicilians are touchy about their young
family members...

6 newborn or veal cutlets
Tomato gravy (see index)
4 cups mozzarella, 1cup parmesan, 1cup romano
Seasoned bread crumbs  mixed with  
  parmesan
  romano
  salt
  pepper
  oregano
  garlic powder
  chopped parsley
Flour
eggwash (eggs and milk)
Peanut oil for frying.

Pound the cutlets.
Dredge in flour, eggs, then the bread crumb mixture.
Fry till golden brown in 350? peanut oil.
In a baking pan, place a layer of gravy,
  then one of meat, gravy, and cheese.
Another layer each of meat, gravy, and cheese.
Then bake at 350? for 45 minutes.
Serve on hot pasta with romano cheese.

Southern Fried Small-fry

Tastes like fried chicken, which works just as well.
In fact you may want to practice cutting up whole chickens
for frying before you go for the real thing.
Whole chicken is much more efficient and inexpensive than buying pieces.

1 tiny human, cut into pieces
2 cups flour
Onion, garlic
Salt
pepper
garlic powder
cayenne pepper
hot sauce, etc.
Oil for frying

Mix milk, eggs, hot sauce in a bowl, add chopped onion and garlic.
Season the meat liberally, and marinate for several hours.
Place seasoned flour in a paper or plastic shopping bag,
  drop pieces in a

Most likely your problem is one shift cable has grease that has become
stickey and dirty.  There are two cables one for front and back and
the other for side to side.  Replace or clean the cable.