I have a similar machine. Mine was made (I think) in 1969. It's a Bolens Artic 75. Everything is heavy duty, as if it was a two-wheeled tractor.
I had a similar arrangement on mine. There was a lever that slid a dog into the driven side of the machine giving you 2 wheel drive. If the snow was light, you could slide it away, and have easy turning. My machine is old, and it always tracked poorly when in left wheel drive, so I always kept it in 2 wheel drive. After 40 years, the springs started to wear out, and it would continuously disengage. When I was using the machine, I'd find myself hopping on one foot with the other trying to keep that lever pushed in. Having been laughed at enough, and having purchased a welder, I cut the lever off and welded the axle solid.
The only thing I was concerned with was having too much traction, so I ditched the turf tires with chains, and replaced them with modern snow tires. They grip ok, but tend to slip/spin before the machine bounces like it used to.
Contents under pressure....