I now use 10W-40 synthetic motorcycle oil.
I use it because oil temps can go over 240F in an air cooled riding mower, lawn tractor, turf tractor, and push trim mower. It has fantastic anti wear, anti foam, antioxidants, anti rust, higher HTHS, and was designed with air cooled engines in mind.
I have a 5 HP push mower(it actually calls for 5W-30 synthetic) an older JD 14 HP Kawasaki turf tractor, a 2008 JD 20 HP lawn tractor. All of these are air cooled and get the synthetic motorcycle oil and Wix filters.
Our Church has a 1989 Honda, liquid cooled turf tractor. I do the maintenance on it and it gets free Valvoline synthetic 10W-30 MaxLife and Honda filters. If the oil and filters for it were not donated, I would use 10W-40 motorcycle oil and Wix filters, if they are even available.
Our 3 cyl, 4640 Ford diesel tractor gets Rotella 15W-40 and New Holland(I think New Holland) filters. A family member fills a 2 1/2 gallon jug from a bulk supply and I believe it is $12.00.