It sounds like you want the studs.
Chains are good for forward traction.
You want '2 link' tire chains where every other link on the hoops has a chain that goes across the face of the tire.
These have good traction front to back but less directional traction, perfect for plowing.
They are supper heavy - there is a lot of steel there.
The negative side is they are more suited for low speeds.
Even if you know what you are doing and install them tight (let the air out of the tire, put the chains on as tight as you can then inflate) and put tensioners something will unhook and the chains will eat an inner fender, brake hose of suspension arm.
I just use the chains, no tensioners and keep the speed down.
Tire studs have less traction but they are predictable for forward and side traction.
Studs don't have issues with eating parts.
And the studs are appropriate for driving at speed on ice.
I run studded tires on my cars.
On road studs are a little different than the ATV/SXS screw in studs but the basic concept is similar.