A lot of variables here.
Long story short, I'm going to assume your stock tires are actually in good shape. Ok tread, aren't 10 years old/dry rotted, etc. Also I am going to refer to southeastern US wheeling. We have mud on everything. Even the rock trails have mud on the rocks. I will not be discussing the bottomless mud pits because those are for your brodozer JKs on 37" tires.
I'm just discussing general trail riding were most of the trails are dirt...and are susceptible to issues once water begins falling from the skies.
The biggest difference you'll notice is climbing muddy hills or crossing thick muddy spots. Also rolling over slick objects. Take a slick log for example. You'd have trouble clawing into the log and climbing it. So you just end up spinning.
On climbs, the second you hit some lose dirt or mud, the front basically becomes useless. Or the rear end just digs in, whichever happens first.
Airing down can help somewhat in terms of increasing traction.
I'd say in dry conditions, you may not notice a difference between stock tires and more aggressive tires. However once the slick happens, you know it.
Slick side slopes. We are fortunate that our trucks are pretty lightweight. However with heavier vehicles or with lack of grip, they can slide. And not like, slide off a mountain-slide, just slide 1ft one way...off the line you were taking...and needed. This sucks.
Lastly, in mud and lose dirt, they just clog up. Then you are done. No amount of spinning or rocking or anything. They are slicked over.
Overall, I have stock tires on my stock 94 4Runner. I typically do not go out by myself, so I don't mind messing up. Done it many times and have rode the magical yellow tow strap of off road forgiveness as I am saved from imminent peril :angel: .
I'd say, go for it. Wheel with other vehicles on stock tires. Learn what the truck can do, get stuck, get recovered. Have fun. Just have good recovery points and good recovery straps. In all honesty, the smittybilt 3"x30' strap is darn good. I've been hating on mine and try to kill it...and it doesn't. For the price, it really cannot be beat.