If it were me personally, I would opt to add weight to get traction that is easily removed if needed (wheel weights, suit case weights, or a weight box).
It is probably hard to get the suitcase weight kit for a Honda as I suspect they are pretty rare by now, but you can build a weight box or attachment to add other brand weights (John Deere suit case weights for example). On your 4120 a used John Deere or Sabre kit might be a bolt on.
In the summer when mowing you are packing the ground because of the extra weight. Depending on tire size you will perhaps add about a 100 lbs of extra weight to the mower with a liquid weight. Do you really want to be mowing all summer long hauling around an additional 100 lbs for more?
In addition, you can add weight in increments with removable weights, whereas liquid weight in the wheels is a fixed perhaps permanent amount of weight.
Adding weight at the wheel cuts rwhp (rear wheel horsepower) because it is 'unsprung' weight. When adding or removing weight to a vehicle it is always better to add/or remove weight that is suspended rather than to the parts that are included in the drivetrain. When you race a vehicle, ever 10 lbs you reduce from the drivetrain (rearend rotating internal weight or wheels - unsprung weight) increases rwhp or vice versa.
Whether or not the reduction is significant on a vehicle with only 20 HP - don't know - but I think you will be able to feel the difference on the seat.
Adding weight behind the rear wheels (suitcase weights or weight box) will also change the center of gravity transferring weight from the front of the vehicle back to the rear wheels. So the vehicle will steer easier as well especially when the blower or blade is in the up position.
Lastly, I think there will be more wear and tear on the hydrostatic drive with the additional ballast in tires/wheels compared to sprung weight - especially in the summer time. That's why there is a fan blade back there - to keep the transmission cool because of all of the heat generated in the hydrostatic tranmission. So in the summer I would want to remove weight - unsprung weight (wheels weights or wheel balast).
Whether or not the hydrostatic transmission in our Hondas is nearly indestructable like those made by Tuff Torq or Sundstrand that are in John Deere 300/400 series - probably not. There are different models made by Tuff Torq and I suspect the hydrostatic in your 4120 might be made by Tuff Torq made for John Deere for Honda - maybe a K46 or one number series higher.
In short, I would go with removable weight rather than tire balast in the tires.