Can I lay ceramic/porcelain tile on my wooden patio using backer board?

I think the expansion and contraction in the winter will be too much, no matter what you do. If this were a floor in conditioned space, then Dur-rock over wood is sufficient . The Dur-rock should be securely screwed down to the sub floor, and a modified thinset should be used. I've set frostproof tile over concrete outdoors with good success. but never over wood.