Call the dealer and see what he says.
It could be the battery or it could be your alternator or charging circuit.
To check which it is, jump start the tractor & then measure voltage at the battery terminals, at a high idle. If the voltage is less than ~13.5 volts, the battery is not going to charge properly and you have deeper problems than just the battery.
You might get a new one for "free". OTOH, if the dealer is far enough away it may be less costly to just go down to Costco and buy a new one for $50 or so.
My philosophy on this kind of stuff is that if it is going to cost me more to have the tractor put on a trailer and moved to the dealership & back than to just troubleshoot it & fix it myself, I tend to just fix it & move on. In less than 30 minutes you should know if it is a bad battery or a bad charging circuit. If the latter, get the dealer to fix it. If not, a new battery could be less than transport to & from the dealership.