My original setup did not have springs holding tension to the chains. However on my first test drive the chains nearly fell off the tires before I had even been driving for a minute. The tension applied by the springs isn't a ton, just enough to hold the chains to the tires. My ag bars are also not very tall and the chains ride over top of them rather than between them (which is probably due to the type of tread, there's probably different treads that allow the chain to slip between the ag bars).Type//style of the cross chains and how tight you run them makes a big difference. Most people run their chain to tight or to narrow for the tire they are on. Really no reason to use any tension springs, bunge cords, etc on the chains to "tighten them up". Running them to tight pulls them down between the ag bars and don't allow the chains to self clean.
You are 100% correct on my chains being too long for the tires. And being just a garden tractor, yes, it's a pretty slow moving application. For a large vehicle you'd want proper fitting chains, but for a GT it's not that big a deal. Even so, the machine does move fast enough to fling the loose section of the chains up and hit the underside of my fender pan.Prattico's chains are too long for the tires. The setup works because you can probably walk faster than the tractor.
(Not trying to to be a jerk, text communication always hard)