The battery used on the trailer winch is a 60Ah 540Ca car battery. I think the "CA" part of this specification is a measure of "grunt" it can give out when starting a car. There's no doubt your car battery would do the job BUT the current the winch takes is high and gets higher as the boat gets closer to the winch, because the cable builds up in the winch drum making it's effective diameter bigger and therefore requiring more torque to maintain the tension on the winch cable.
I've not measured the effective voltage at the winch. The winch slows down significantly towards the end of recovery, indicating that the current demand by the winch motor is increasing (as the torque required goes up) and this cause a voltage drop at the winch motor (V = IR and all that stuff). The battery is less than a metre from the battery and the wires are about 1/8th inch dia copper, permanently connected at each end (sorry about the mix of measurement units).
This is a long way round to say that, if your car battery is at the front of the car and the boat and trailer at the back and you're going to use croc clips for the connection, you'll need awfully fat cables between the battery and the winch.
Incidentally, I considered using the "fridge" wires on the "new style"13 way trailer connection to charge the winch battery on the trailer but didn't do so because the b*****s who fitted the 13 pin socket on Martina (the car) only wired up the usual 7 pins! Also, I would have needed to make sure they were disconnected before using the winch otherwise I'd probably burnt out the cables in the car harness! Judging by the state of my memory these days, this was just about guaranteed to happen!