You would need to verify that the solenoid's duty rating equals or exceeds that of the winch. Warn should be in a position to supply that info.
For reference, Warns publishes that their 12K winch draws 440 amps at max rated load, and that the winch can only be operated for 30 seconds at that load, and then must be off for 10 minutes.
So, if you were planning to install the 12k winch, the first question would be, is the solenoid rated to handle 440 amps for 30 seconds, with a subsequent rest period of 10 minutes?
Overall, the duty information on the 12k winch above is rather sketchy. A more complete duty spec would specify how long the winch can be run at less than max level of load - I.E. graph of amp draw and allowable time of operation versus load. Then you would want to see the same type of duty graph for the solenoid, in order to ascertain that it can handle the same duty cycle as the winch.
I didn't plan on installing an in-cab winch control. So since I had to leave the cab anyway to operate the winch, I went with a heavy duty marine switch in the engine compartment to connect/disconnect power to the winch. You can check out my setup in post #11 on this thread
I used a marine disconnect switch also. 200 amps continuous, 300 amps intermittent. Has the added advantage of allowing me to connect the battery, 200 amp alternator, and winch all together (via #2 AWG wire) in the "Both" position so that I can leave the stock 30 amp electrical system intact. This way I don't have to worry about burning up the stock fusible link, ammeter, or wiring during heavy winching.