Well your choices are as follows. None of them are cheap.
1- Put in an Optima Yellow Top type deep cycle battery. Deep cycle batteries are designed to handle longer steady discharges and recharges. You would still need an adequate re-charge time after you are done winching, don't just pull it out and then park it. Leave it running so it can recharge completely. In this case, the battery is picking up where the alternator falls short.
2- Put in a high output alternator and an overdrive pully. If you get one that will handle nearly the complete current draw of the winch, you will not be drawing on your battery at all. This will be very expensive but it is the most ideal and powerful solution.
And even better, do both.