You do not have to worry about damaging anything in the drivetrain of a Case garden tractor because it is designed to protect itself from overload. The gears used in the two-speed axle are huge and very strong as are the axle shafts. The Onan engine powers a fixed displacement hydraulic pump that circulates up to 10 gallons of oil per minute, if the engine is running at full throttle. The lever on the left side of the steering wheel operates a control valve that diverts either a portion of that circulating oil or all of it to the drive motor that is bolted to the side of the trans-axle. The control valve has a built-in relief system that will open up and allow the pressurized oil to go directly back to the reservoir IF the pressure in the system exceeds a pre-set value. This is what prevents damage to all of the components.
That said, I need to caution you on a few things.
1. Case tractors made before 1986 did not come with a built-in "Holding Valve" however, many of the earlier tractors were fitted with an optional, external Holding Valve Kit. This valve prevents the tractor from being pushed by weight and gravity while descending a grade. If you intend to pull cars on fairly flat surfaces, then control should not be a problem. We both know that power brakes on cars take a lot of pedal pressure to operate them if the engine is not running to provide vacuum or hydraulic assist, so err on the side of caution. The brake pedal on the left side of the Case tractor is actually a "parking brake" as opposed to a "service brake" and it only works well when it is in good condition and properly adjusted. All the same, do not mistake it for the equivalent of a pair of drum or disc brakes on the rear axle of a full sized tractor.
2. Case tractors with the large rear wheels like the 446 have been known to exhibit a failure in the rear axle. This is something that you should be aware of now. The problem stems from the fact that there is a minor flaw in the design. The differential carrier is a two-piece unit with the Hi and Lo Range gears bolted to either side of the carrier by way of four 3/8" Grade 8 bolts. The carrier halves and the gears SHOULD have had dowel pins as part of the design but alas, that did not happen. All of the torque must be handled by the four bolts. Depending upon how the tractor was operated, the bolts have been known to loosen slightly and then shear off. When a bolt head or nut shears off, it drops to the bottom of the trans-axle housing. There is not much room between the large Lo Range gear and the housing. If the broken piece of bolt migrates to the spot where it becomes jammed between the gear and the housing, the cast steel housing looses the battle and a hole, along with spider cracking is often the result. Yes, it can all be welded back together again but.....an ounce of prevention is worth a pound of cure. In other words, it is advisable to drop the trans-axle housing out of the tractor and deal with this potential problem NOW. If you wish to know what to do, then send me a PM.
3. The ability of the 446 to move cars around safely under all conditions is dependant upon setting the tractor up properly for the task. Traction is the key issue. One way to increase traction is to load the rear tires with a product called Rim-Guard which is actually beet juice extract that will not freeze, is not toxic, will not damage tires or rims and is almost as dense as Calcium Chloride. The 2nd way is to obtain cast iron wheel weights for the rear rims. Those can be obtained quite often from local agriculture equipment dealers that have been around for a few decades or more. Combines and full size Ag tractors that came with 15 or 16 inch rims, often used cast iron wheel weights and the bolt pattern is identical to the Case rear rims. Those weights can add 100 to 160 pounds to each rear wheel and they make a world of difference to the traction and overall stability of the Case Hi Wheel tractors like the one you have.
Tire choice will depend on whether you are using the tractor on paved surfaces or on terrain that can be muddy when wet. Snow/ice can be a factor here so a good set of 2 link tire chains should be considered. I doubt that Ag bar tread tires would be of benefit to you since soft ground is not going to be driven upon.
The 446 will serve your needs very well providing you set it up properly at the outset. It's a tool like any other tool. It has its limitations but when used properly with an understanding on the limitations, then I believe you will be very pleased with it.