How hard will it be to pull out a 30 year old Dogwood tree from the ground with a 4x4 truck? (if dig around it a few feet deep)?
Try a D9 CAT.
It can be done but it would take A LOT OF DIGGING. You cannot skimp on the digging part because your truck isn't as tough as you think. If you haven't cut the tree down yet, then leave about 3-4 feet of trunk above the ground for more leverage. Cut notches around the remaining trunk for the tow strap to nestle into. Or, drive BIG bolt or nails into the trunk so the strap can't slip off the top. Gentle tugs are all that's required from the truck. If using a chain or other non-stretchable device, place a heavy throw rug over the center of the chain. In case it breaks, the rug prevents it from flying up and through your back window. If the tugs don't work, dig some more and keep digging.
You will wreck your truck on a 30 year old tree!
Trees are a lot tougher that you'd think. A big tractor might be able to rip it out.
What are you smoking? When removing small trees or shrubs from the ground, it isn't the power of the truck, it is the weight. My Dodge diesel weights about 5,000 pounds. When pulling out shrubs, you leave slack in the chain and take off, using the moving weight as power. You will destroy whatever truck you are using.
If the roots are severed when you dig, you don't need the truck at all. If they are not, you have never seen a truck that can handle it.
Use a winch or pull-along.