You won't like this, but removing the radiator is 10 times the job it really should be. Honestly, I think the front end of the 1010 was designed by about 6 different engineers and they just did their best to fit it together during production.
Here's the obvious part: Take the off the hood, front hood support bracket, grill, power steering hoses. You need to remove the top piece of the power steering stack. That's the one with the worm gear. The second big piece, between the worm gear and the steering cylinder, stays bolted in place. Start spraying everything down with penetrating oil a few days before.
Remove the 3 bolts on the tube that goes through the radiator hole and connects to the top of the power steering stack. You can't remove it yet, but leave it loose. There's shims in there also that set the slop on the worm gear, so watch for them falling out later in this process. Remove the top cover of the worm gear piece and pull out the shaft. There's a splined coupler at the bottom with no snaprings or set set screws. If this upper shaft doesn't just come right out, the shaft is probably seized together in the coupler. Once the shaft is out, you can remove the housing that it was in. **Note, the book doesn't say you need to take this shaft out! Damned if I could make it work without doing so! ** However, you can't remove that piece without moving the radiator also, so you need to remove the lower radiator bolts and hoses and lift it slightly while pushing it towards the engine to make room to tip the worm housing out. Its tight, and its stupid, but that's how it comes out. The book does kind of tell you this part, but its really the key. Get another person to wrestle the radiator back while you are trying to pull the worm gear housing.
Oh, and after the worm housing is out, remove that tube cover in the radiator hole (the three bolt thing and aforementioned shims)
I would suggest marking positions of the steering sector at the bottom (wheels straight ahead) and the worm shaft before removal so it stays in time. If you have to disassemble the next section with the cylinder, there are some timing marks on the rack and pinion....but hopefully you don't have to get that far.
Next, you'll need to remove the fan shroud and leave it in place so you can pull the radiator out. Otherwise you can't maneuver it around the fan.
And finally, you might get lucky and are able to do all this while leaving the power steering valve in place. When I did this, I happened to have the valve off already, and it definitely helped. Just the extra room you need to push the radiator back. If you have to pull the valve, don't be surprised if you have to pull the tank to get access to the bracket bolts. In short, you will have half the tractor stripped to get the radiator out.
The holes in the gas tank and radiator for the steering rod were just colossal design fails in my opinion, and I could almost forgive the gas tank if the radiator didn't have a hole also.
Sorry for the meandering description. Anything I forgot was probably scrubbed from my memory by the shear trauma of the whole event. Basically if you see something that is near the radiator and think to yourself "Nah, there's no way I would need to take that off just to get the radiator", then yes, unfortunately you need to remove that part also.
The steering stack, worm gear and rack/pinion, are supposed to be filled with gear oil. I repacked mine with grease.