You can run a big battery if you put it under your drivers seat.
Seems odd that you're not getting enough power for winching from a dual battery, though. Are you running your motor while winching?
If you can run the engine, that's a good idea for a couple of reasons, but keep in mind that the engine's charging system can provide about 50 amps max, and that's at 5,000 rpm. Then consider that the Warn 4,500 lb winch on my SE draws about 216 amps at full load, 135 amps at 2,500, 71 amps at 1,000, 49 amps at 500, and 28 amps just winding the line back in with no load.
You can see that the darn winch uses a bunch of current. It's a compromise for sure. The second reason to run the engine, if you can, is after winching you don't want to be in a position where you can't start the motor - - if you have a True isolator (or similar) that will allow the primary battery to "help" with the aux battery load while still keeping the main battery from suffering deep discharge.
Lead acid batteries lose service life when heated. "This reduces service life at a rate of 50% for every 18°F (10°C) increase from 77°F (25°C)". When locating a battery, especially in what is likely to be a hot environment (such as under the seat), reduced service life may be a consideration.