When I bought my tractor used, back in 2002, it came with rear chains. But after trying it one winter, I purchased chains for the front wheels. What a difference that made. 4x4 is the way to go.
25 years with a Kubota Grand L3710 and I've always chained up just the rears, with no issues. I'd be worried about breaking something if all 4 corners where chained up. I have a rear mounted snow blower, but still push a fair amount of snow with the loader. If steering traction becomes an issue, I'm going too fast. I could always use the steering brakes, but the brake pedals remain locked together 99% of the time.
My problem was always steering, not traction, so I did fronts only to save on cost. But I had a blade which was really hard to steer due to the side loading. I now have a blower on my CTL and side loading is not a problem. Total traction might be if it were a tractor. I’d still try only fronts because good chains can be spendy,