It will work with wood. There are plenty of commercial campers that were (still are?) designed and built with wood frames. They might use a bit tighter grain higher quality wood that what you might be thinking of using. I am not sure that wood is that much lighter than steel and I am not sure it is cheaper. I was amazed at how cheap the 20 foot sections of 0.062 1x1 and 1x2 were. We went to a local steel yard (Everett Steel in Washington). Less than a buck a pound, so even with waste you could build a 500 pound steel frame for under $600. We spent about $1300 on steel but our camper is huge and we used 0.125 wall thickness for certain members which I have come to believe was overkill.
S&S campers are all wood though, aren't they guys?