Hydrostatic mower drive belt - Troy Bilt Horse
It's fairly typical for lawnmowers to have guards like part #57 which make it difficult but not impossible to get the belt on.  They're more concerned with making it difficult for the belt to come off.  Though, this also helps keep it in place while you fiddle with the other end.  You may need to strongarm it a bit, but try to bend them back to the original positions.

If you really want to get the fan off, you need a crow-foot wrench and will probably need to hold the pulley with a strap wrench and work against that.  Don't be surprised if it's a reverse thread. The pulley will be splined to the shaft. 

I've recently seen a suggestion to hold the pulley by twisting the belt with a flat nail bar.  Then put a short 2x4 between the nail bar and frame.