Ages ago it was done all the time to make farm equipment.
Worked on a farm with a gadget made from an old school bus that had (3) 4-speeds in it. The original flathead 8 was toast, but was left in as a way to mount the 1st trans. Input power was from a 16hp one-lung Wisconsin with a 6:1 gearbox, with a double pulley. Two "B" belts were run from there down to the original crank pulley on the original motor, now without pistons. This was used to haul around 20 pickers and handlers and a few tons of produce at a very slow walk, up to a medium walk as the vines were picked out toward the end of the season. Whenever possible, the engine was kept at whatever idle that would keep it from stalling to minimize fuel consumption. It replaced a briggs 8hp, also with a gearbox that would also do the job, but at half throttle or more and so used more gas doing it, as well as breaking down more often.
All this to say that 8 to 16 hp, geared down, can do quite a bit of work.
You didn't say if you were planning to reuse the car motor or go with a small engine. If a car engine, I'd be leery of anything much over 2L as being way overkill and capable of breaking parts. Even with a smaller motor, I'd be tempted to add a belt-driven governor both to make the tractor more useful for operating, and to keep you from the temptation to apply a lot of power and break parts.
If using a small engine, don't forget that you can apply more reduction in the first stage of the belt into the first transmission. If you use a "B" section belt like a riding mower uses (except yours will likely be shorter), especially one of the kevlar wrapped ones, you will likely be able to handle most of what any reasonable sized small engine can put out. A lot of the adaptation will get simpler if you use a small engine and a belt drive/belt clutch.
You mentioned mowing. Did you intend to have a "real" PTO, or a mower with its own engine, or were you thinking of ways to drive the PTO from a separate clutch off the "front" of the engine, so you could stop the tractor while the mower "chews through" whatever it was working on? Did you have plans for some sort of overriding clutch, like the 8n/9n guys use, to keep the flywheel effect of the mower from pushing the tractor through the PTO driving the gearbox even after the motor is clutched out?
Just how much thought have you put into the other adaptations that are needed to go from just moving people around briskly to operating implements at a slower pace, besides just slowing the machine down?