On your 3/4 ton the transfer case should stay engaged in 4wd with engine off.
The 1/2 tons with the transfer case with an "auto" mode will not stay in 4wd when the key is off.
That was my thought as well with Auto 4 wd, 3/4 ton would be different. What about the manual 4 wd? don't know. The streets around here are under ice, We had rain on top of hard pack snow and them it dropped to -20 , Not a rare thing up here . I run studded winter tires in winter.
Had a fellow slide into me a few years back, all 4 wheels locked, and he did not understand that you can't steer if the wheel aren't turning
I don't use salt much, it is real hard on cement, and grass, I have some "pet friendly stuff, don't do much on the ice i cold, but it is good for traction, and will soften the top some.
Mine sits in the garage, but friend has a real steep drive way, hard to walk on it in winter.