When the winch fires up, the voltage of the entire bus will drop. Some power will flow into the bus from the rear batteries, some from the front battery, some from the alternator.
The rear batteries are probably deep cycle, the front probably a cranking battery. The cranking battery will have a lower resistance and can supply more amps faster than the rear batteries. The alternator is even faster at dumping amps into the bus than the cranking battery.
As noted, a 12k winch can draw as much as 450a at FLR (full locked rotor). It depends on the motor and the gearing, and it's unlikely that you'll ever load it until it stalls. So that 450a number is probably not a big enough deal to really worry about.
A 50' or less loop of 2/0 welding cable can handle up to 500a at a duty cycle of 60% or less (and your winch might not be rated for a 60% duty cycle anyway), so no worries about the cable.
The 150a breaker will probably pop if you load that winch up pretty heavy (and it sure will before you hit FLR and it stalls) - but maybe not. If it does, go bigger.
What's the solenoid rated at?