Well if it is tripping the GFCI, it is obviously leaking current to ground which is passing to the concrete thru the impliments. It dosn't have to be much of an imbalance to trip a GFCI. So the wiring to the heater on the tractor could be creating a circuit thru damaged insulation. When you replaced the heater, did you replace the entire wiring harness, or just the heating element? Dirt/crud moisture in an area where the wire runs along the chassis, and a hairline crack in the insolation and you have a low flow circuit to chassis ground...
Another thought is the heating element is damaged or improperly assembled(not constructed to NEC) and the conductor inside the element is in contact with the coolant, allowing a circuit to be formed with the coolant. This could allow a small ammount of current flow to ground thru the coolant in the engine to the chassis and on to ground. Is the wiring to the heater a 2 wire or a 3 wire circuit? If it stops tripping the GFCI when the blades are lifted, I am guessing 2 wire? If it was a 3 wire, it would pass this current back thru the third conductor(ground) and it would trip regardless of blade position. The problem with lifting the blades onto rubber is that you are now allowing this unknown ammount of leakage to build electrical potential in the tractor. This potential is now waiting for access to ground, perhaps thru you when in damp shoes on the concrete reach out to touch the frame and complete the circuit to ground...
I run my tank type heater off of a GFCI outlet without any issues. I am on gravel under a lean-to alongside my garage instead of concrete, but it is on a 3 wire circuit. In this type heater, the ground wire is connected to the outer shell of the heating element so if a circuit is formed that could contact the coolant, that current quickly passes to ground that would trip a GFCI. I have never used a rad hose type on a GFCI, but they are basically the same hooped type heating element so the conductors should not be in contact with the coolant. The tank type does offer greater isolation thru it's smaller hoses and remoted location.
If you have a meter, you could plug the tractor heater into the GFCI with the blades raised and carefull not to make physical contact with the tractor, measure the voltage between the tractor frame and the third round hole on the GFCI outlet, to see how much potential the tractor is reaching... If you have a shorted harness(shorted to chassis) on the tractor, you will probably see 120V on the tractor frame when making this measurment. Nothing like grabbing a bare live wire/tractor to wake you up in the morning before you go plow snow
An electrician who comes to look at this and suggest you isolate the tractor frame from ground instead of helping you resolve this potential safety issue ought to have that type of wakeup...