Afraid I do not agree with the Bungee cord option. You do not want a chain to come adrift while working,
Not sure if my solution on a Ford 6000 will work for you on a small garden tractor, but this system overcomes all the problems of securing everything. It consists of a steel "ring" on each side of the tire - nothing fancy, just strips bolted together into an octagon shape. The chains are attached to the rings simply by passing the chain through the bolt that is secured with a Nylock nut.
I have had this arrangement in use for several years now and it has worked perfectly. Look carefully at the picture and you will see the rings on the insides of the tires. They are duplicated by identical rings on the outside faces.