This cold winter we are having here in upstate NY (as well as the rest of the country), finally killed the factory battery on my 10 year old, JD 4120 (same tractor as yours, but with fuel pressure cranked down a bit). During those years, I never used a trickle charger, or any kind of charger and, with one exception, the tractor always started good in the winter. My tractor is stored in an unheated barn, but I almost always use a block heater, for at least 1/2 hour, prior to winter starts. With that block-heater on, for just 1/2 hour, in temps as cold as -10 F, the tractor starts as well as it does in mid-summer.
In my opinion, based on my own experience, a trickle charger or battery tender should not be needed on this series of JD tractors. A block-heater, however, is recommended for cold-weather starts. This device will reduce engine wear by bringing up the oil temperature, allowing it to reach bearings and other critical areas faster than a start using nothing, or just the preheat feature on the ignition switch. You definitely have a defect, or some type of problem, if your battery failed to start your tractor that soon. It is probably just a defective battery, but may be some type of voltage leak. Do you have a block heater?. If not, I would be more concerned with premature engine wear in the winter than I would of any electrical issue.
The time my tractor did not start good, was a premature starter failure when the tractor was about 3 years old. I replaced the factory installed, defective, Bosch starter, with an aftermarket "Powerstrike" (1/3 the cost of the Bosch at the dealer), and the tractor has started great ever since. When that factory starter failed, I may have had the "clicking" sound that you describe, but I doubt your newer tractor still uses that older, defective "Bosch".
