Turn on Auto LSD.

 

Strange that the auto LSD does not operate if you are in 4WD. It would seem to me that you’d want that possible combo. https://www.wheelsjoint.com/how-to-enable-auto-lsd-on-toyota-tundra/

 

This article is wrong. Auto LSD does operate in 4wd.

 

What model truck is it

 

What you want in snow and ice is traction control with 4WD. The issue is that 4WD traction control on the second and third gen (which I presume you're talking about, could be wrong) requires a lot of wheel spin to trigger, as it electronically tries to behave like Auburn LSDs which require a significant difference in wheel spin between wheels (like 100 rpm, at the tire, which is like 35 mph+).

If you want all four wheels to spin, slowly, on any 4WD vehicle, you want locking differentials front and rear. The 2022+ TRD Pro comes with a rear locker, but front diffs on anything but a Mercedes G-Wagen are an aftermarket thing.

4WD is not a magic solution to traction issues. It changes the problem. This is why military vehicles and overlanders all carry shovels, traction pads, and sometimes traction materials. And for the love of God, four-wheel go is not the same as four-wheel stop. My Tundra has pulled out many a bald-tired Subaru and BMW X-series from ditches, complete with their bewildered drivers.

 

four-wheel go is not the same as four-wheel stop.

Millions of consumers have been brain-washed into believing that full-time AWD (all wheel drive) is somehow, vaguely, "safer" than conventional FWD or RWD. I'll explain "you've always had 4WD brakes ...", which also seems to confuse them

 

Here is an old school solution. It is true that at best, when stuck ,one of the front and one of the rear wheels will spin, and the LSD does not really seem to help much. However, back in the old days when everyone drove rear wheel drive large cars, they would get a piece of carpet about 3x3 and put it in the trunk. When they got stuck, they would stuff the carpet as hard as they could into the tire/ground gap in front of the tire and that carpet would give you enough traction to get unstuck. It works amazingly well!

 

@Mikecol, I was referring to the "full time AWD" with the viscous-y transfer cases, which seems to be all the rage on mid-size SUVs nowadays.

 

These are some videos I show my students:

The Eaton locker requires a speed difference to lock-up. They were (are?) used especially in GM vehicles. Most manufacturers, if they offer limited slip, use clutch packs on the side gears. Auburn gear traditionally used cone style limited slip, which when worn cannot be rebuilt. They do last a long time though. A third type of LSD )limited slip differential) is a Torsen or worm drive style. Originally used in the USA on military Hummers, I believe. There is also a manufacturer in the United Kingdom named Quaife of the worm style.
A modern vehicle with full time 4wd has three differentials, one in each axle and one in the transfer case. With this system you can actually have only one tire spin even in 4wd. A part time 4wd (off-road only) either locks the center diff or doesn't have one at all. They call it part time since it should not be used in high traction conditions (highway driving), only in off-road or loose terrain.
Lockers are best, but they have to be able to unlock for turning so modern vehicles often use electricity applied lockers or something like the Eaton. There are also some cable (Ox) and air (ARB) actuated lockers.
I have Lock-Right (Powertrax) lockers in a Jeep Cherokee, they unlock when off the throttle, and it is very capable. In low traction conditions all four tires spin. Even when trying to climb a solid granite "hill" all four tires would spin because I didn't have enough traction to overcome gravity and mass.
I would really like to put a locker in my '23 Tundra, but I haven't located an aftermarket option yet. One day.

Just my two cents.

 

Back to the OP's original question, once you are stuck it is unlikely that you will be able to get 4WD to engage. The vehicle has to move in order for everything to line up so that 4WD can hook up. If you can rock the vehicle back and forth it may be enough to get into 4WD.

 

My Tundra came with aftermarket with a Auburn Gear LSD in the rear that is worn out and getting some chatter. I want to put in a torsen diff, but one is not made to fit the 2nd gen Tundra. I'm hoping someone comes out with a torsen (Nitro for $1700?) or I may go with and eaton E-locker. Any recommendations?