Don't use 4-wheel-drive on a soft-roader unless the wheels are
actually spinning, otherwise you risk blowing the transmission.  When
the manual means "slippery" it doesn't mean tarmac roads, slight
covering of snow or not.

It's a pick-up is it not?

Because it is not slippery. These basic working trucks have a similar drive
system to old Land Rovers which dates back to the first half of the last
century. This system is designed for field and track work, not roads. Not
even icy or moderately snow covered roads. As you have found, they wish to
travel in a straight line when 4wd is engaged. This makes it potentially
dangerous to use it with 4wd engaged just on moderately slippery roads, such
as those with a light covering of snow, because you will find it wishes to
go straight ahead on corners.
The way around this is to buy a vehicle that is suitable for your purpose.
One which either has full time 4wd with a centre diff to allow turns [Land
Rover and Toyota, some Subaru and Audi etc] or automatically engaged 4wd
such as some Honda vehicles and Nissan crossovers.

I read in the manual, that you use 4H for slippery road

You should only use 4wd [4h or 4l] when there is a real risk of getting
stuck. Either should be engaged *before* you get stuck. It doesn't matter
whether you use 4h or4l and the difference is only in the gear ratio. Choose
the gear that gives the speed that is suitable for purpose. I have just
bought a Ford Ranger with a similar drive system but I have a farm. That is
where your truck is designed for, bare land not metalled roads.

No it should not. It sounds like you have the wrong type of vehicle.

Change it for a vehicle that does what you want and need. A pick-up is a
commercial vehicle and an Isuzu especially is not my idea of an everyday
road car.
Sorry to be the bearer of home truths and what may be bad news to you. For
what its worth I think part-time 4wd is an outdated crappy design and I
can't understand why they don't fit full time 4wd to all these types of
vehicle. The only pick-ups that I can think of off-hand with full time4wd
are Land Rover and the luxo versions of the Mitsubishi L200. The workaday
ones have to 'make-do'.

Huw

The road ain't slippery then. Or there is something drastically wrong.

One presume that your steering turns normally? Does your vehicle have
axle diff locks? Even so, it shouldn't take that much power to
override their effect.

I've been driving 4x4 for 40 years and I've never come across the
situation that you describe. Even in an old Landie stuck in 4x4. In a
modern vehicle with old technology you shouldn't even notice it until
the transmission goes bang :-(

Seriously. Only use 4x4 high on wet grass, snow (lying on the ground
and not showing tarmac), gravel tracks and mud.

Icy roads are a bit of a red herring - you cannot tell when they are
icy and you can be driving on long stretches of tractive tarmac in 4x4
winding your transmission up which can damage it.

The editor of one of the 4x4 magazines, some time ago, was towing a
Camel Trophy Disco to an event, and had driven with the tow vehicle in
4H - for about 200 miles. He had said that the transmission felt odd.
Entering the event, he had to tow past a queue of visitors. In doing
so the offside wheels of the tow vehicle dipped off the tarmac onto
the verge, there was a bang from the transmission as they wheels lost
grip and the whole rig jacknifed putting the Disco being towed on its
side.

If the tarmac is slippy you can have some fun in 2wd anyway :-)

4L is for when you are crawling over really rough terrain or
descending really steep hills off road, or towing much bigger vehicles
for a jump start or towing on slippery conditions. or, when you want
to pour gallons of fuel down the inlet manifold for fun - try it, put
your computer on instant fuel consumption and see what happens when
you drive across a field in 4L :-)