If you're dealing with a system that was originally 6 volt, and the wiring is in good shape, the wires should carry the halogens just fine. Generally, 6 volt wiring was a gauge or two bigger than the wire used on 12V systems. Good-condition 12V wiring will work, as long as it doesn't get warm to the touch anywhere.
HOWEVER- - - -if the old rubber-insulated wiring is deteriorated, or you've got corroded connections everywhere, and/or a dirty dimmer switch, all the gremlins will come out to play when those halogens start drawing extra amps. Do a thorough inspection of the system, from the ammeter terminal to the headlight switch, to the dimmer switch, to the lights, and then wring out the ground side, what we used to call an IRAN inspection in the military (Inspect and Repair As Necessary). Once everything is up[ to snuff, you'll wonder how you ever got along without all that bright light.
Jerry