To doze materials you need to be able to apply a very large tractive force to the dozer blade at zero speed, ranging up to a very low speed. This is at the opposite extreme to what mowing requires, which is applying just enough tractive force to move the mower itself with almost no resistance, at "mowing speed". The Greenfield tractors/ride-on mowers have a transmission system which I rather admire for mowing purposes, but it effectively runs one side of a clutch at the maximum possible vehicle speed, and the other at the actual vehicle speed. Whenever the vehicle is travelling at less than maximum speed, the clutch has to be slipping enough to account for the difference in vehicle speed. Trying to doze with that transmission would be similar to trying to pull a caravan with a car that had a manual transmission permanently locked in fifth gear. You would apply very little force to the dozer blade, but would burn up the clutch in a very short time. Greenfields have a car-sized clutch in a tiny ride-on, but even a big clutch cannot compensate fully for a very high-slip ratio while transmitting maximum torque.
If you want to use a garden tractor as a micro-dozer, you need a tractor that is designed to use "ground engaging" attachments, such as a plough, ripper etc. This would mean having an extremely strong transmission with an ultra-low low gear, or one of the expensive industrial-strength hydrostatic transmissions. The hydrostatic transmissions on ride-on mowers are unsuitable, but some of the garden tractor ones may be suitable. Careful investigation is necessary to choose a suitable tractor - don't believe the sales brochures.
Is your Toro Wheel Horse a 12-32XL? If you tell me the model I can look up the type of 5 speed transmission it has. In principle a 5 speed transmission might have a low first gear. Less likely but possibly, it may have a substantial torque capacity and a decent clutch. If it has all of those, and if its manufacturer recommended it for ground-engaging applications, it could be suitable. As I understand it though, the Wheel Horse XLs were "lawn tractors", not "garden tractors". Usually only "garden tractors" are rated for ground-engaging applications (and not all garden tractors, in fact - generally the heavier, more expensive ones).