Ok, first of I am a complete newbie to this tractor as I inherited it with my house and I love it!
What am I missing, because the wheel will not come off!
Yes, at that point, it is supposed to just slide right off. However, yours may have some corrosion between the shaft and the spacer (spacer is between the bearings on the inside so you do not compress the bearings when you snug the nut.)
I would suggest soaking BOTH ENDS of the wheel/shaft interface with a rust-disolving spray (Liquid Wrench) and allow it to soak for several days. Re-apply a couple times a day and tap with hammer to set up vibrations to distribute the liquid.
When you are ready to attempt removal, place 2-by-4 long enough to touch rim on both sides on INSIDE and hammer against that. (attempting to force the wheel off the axle.)
BEWARE: The rust-disolving spray will contaminate the bearings. You will have to remove the bearings, degrease them and repack with grease.
ANOTHER OPTION: (which will not contaminate the bearings) Put the nut back on and reassemble what you have removed. Install tube into the wheel WHILE INSTALLED ON TRACTOR. (They do this on full-size tractors)
I assume you realize that castle-nut should be only finger-tight. NO MORE! Then install the cotter-pin. (loosen nut just enough to find an alignment with hole)
I was lucky with my G5200HST and the wheels slid right off. Then, I pulled on end of the tire off the rim and slid a tube in each one. No more flat tires.
NOTE: My G5200HST has grease-nipples on the front hubs. Your photo does not show this feature on your wheel. Infact, I do not even see the threads for the castle-nut. Does your wheel have ONLY a cotter-pin holding it on?