4 wires with 6 gauge power wires is called 6/3. It's considered 6/3 with a ground. Having a ground is a nonspoken constant. Yes, the ground is always smaller. It doesn't have to be as big as the power wires and the neutral wire. Especially if you use a neutral wire, the neatral wire takes some of the "left over" electricity back into the breaker box instead of sending to ground and thus wasting it. Going with the outdoor wire (called UF) is definately the way to go. Then you don't have to run it thru conduit, which some inspectors are picky on anyways.
Pop N, your wiring is perfect for a 55 amp service and 30 amp outlet and going with a subpanel box for garage/shop is the best way to go. I don't actually own a welder. I have set many customers up with wiring them tho. I went from being a Nissan parts manager to a manager of a fortune 50 home improvement/ hardware store. I'm just saying what is recomended not what can work.Although I seriously doubt that your welder is pulling 145 amps. It may be the rating of the welder but not the amperage draw that it needs to operate. Or your just not using it to it's fullest. Remember 7lbs. of boost is what Nissan recommends but we all know you can get 15lbs. with ease.