It's not a problem at all to hook up two 12 volt batteries in parallel. My NPR has two, my Dodge Cummins has two and I put two 8Ds in my boat. The best way to make sure they are charged to the same voltage is to hook them up pos to pos and neg to neg, and then connect the charging cables one to the pos on one bat and one to the neg on the other bat. Otherwise they will have slightly different voltages.
Whatever type battery you choose, deep or starting, make sure they get charged properly after use and stay charged. The worst enemy of the typical lead acid battery is being left undercharged. This causes sulfation and reduced capacity. If they are connected to the truck batteries they will be charged to about 14.1 volts and held there when the truck is running.
I don't see why you can't just connect your winch to the truck's batteries with a disconnect switch and have the engine running when you use the winch. You probably have two group 27s right there looking for something to do. Then the alternator will recharge them automatically after each use and you won't have to carry around an extra battery. This is how I ran my Warn winch on my truck and I put a very heavy demand on it at times, much more than simply pulling a car up onto the bed. Never had to worry about the condition or charge of the winch battery. You'll have the full output of the alternator to help carry the current draw and the bats are right there behind the cab.
If you do go with a separate battery, use a starting battery because the winch load is similar to a starting load. Heavy short term amp draw. Deep cycle bats are more for slow steady draws like running lights, navigation equipment or trolling motors. Either way, keep them charged after each use. Only nicad batteries need to be run all the way down before charging, not lead acid bats.