The radio may have two positive wires, one for "keep alive" for memory, the other for operation. The keep alive would normally go to always on power, and preferably not the battery that powers the winch, as that can get sucked way down.
For powering the radio on, you can use two diodes. Both banded (negative or cathode) ends will go to the radio's positive power-on wire. The anode (no band) end of each diode will go to positive voltage, usually ignition switched for one of them, and aux switched aux power for the other. It will behave thusly:
If the radio is turned on, it will come on with key on. If the "radio aux" switch is turned on, the radio will play with that switch on irrespective of key on or off. Neither battery can feed into the other. If the aux power radio switch is left on and the key on is turned on, the radio can take power from either battery (mostly favoring the one with higher voltage), but even so, it won't cause a back feed . . . if the key is turned off, the radio will stay on until the radio aux switch is turned off (or the aux battery is drained!)
