Thanks, I appreciate the replies. I think I'll put the old battery back in the tractor and use the car battery to power the winch separately.
Better be safe than sorry!
I think you missed the point .
The charging system should be able to handle recharging the battery after you have used your winch , depending upon the size of the winch and how often you use it .
A starting battery can provide amps up to the CCA rating of the battery which should be around 250 to 330 for 1 minute or any multiple of that , like 125 A for 2 minutes , 62.5A for 3 minutes etc etc etc.
The limiting factor is the gauge of the wires.
When the winching is over your mower will see a flat battery , 1/2 flat battery etc and will run as long as required to return the battery to fully charged.
Now if you only winch occasionally no real problem
If you do it every day then you will burn out the alternator because it is always running at full output and it is not designed to do that.
If you run the winch with the engine running the alternator will see a massive load & try to provide the power and again burn out in a very short time.
If you talk to an auto electrician then they will tell you the fastest way to wreck your alternator is to run the vehicle with a flat battery .
People who do not try & maintain their batteries over winter & jump start on their first mow will bring their mower to me as it stalls the instant they turn the blades on so they think there is a problem with the PTO clutch .
In reality the alternator is overloaded & can not keep up ( in theory it should be able to but in practice it can't ) so voltage drops & carb solenoid shuts down .
I have probably replaced 100 or so burned out stators & every time the owners admitted they had been running with a flat battery ( because mower batteries are more expensive than car batteries )