The "plys" will depend on the tire design and ratings. The bias ply tires will have the plys running crosswise diagonally on the tire carcass, a radial will have the main plies running with the circumference of the tire.
Most R-1, R-3, R-3 and R14 tires will be constructed with 4-8 ply ratings regardless of construction design. Even then those are just "ratings" not the number of actual plys.
Many of the R-4 tires will have a higher ply rating, 8-12 are not uncommon making for a stiff carcass with less flex when inflated to design specs., also resulting in a smaller foot print on the ground.
Skidder tires are constructed with several feathers different from tractor tires, such as rubber that is more cut resistant then that used in ag tires. They are also often used with chains for traction enhancement year round.
In many cases stronger sidewalls result in stiffer lower traction tire foot prints. So it ends up as a balancing act of the desired characteristics.
More traction or tougher, which may be effected by the desired use of the tire, tractor, loader, skidder, all different performance issues.