Doug - the guardrails between the running rails were usually made of lighter rail, probably discarded because too light for the railroad’s traffic anymore… Usually spiked upright, but I’ve seen guardrails lying down on their sides as well, with a timber under the railhead to keep the guardrail level and the flange adjacent to the running rails, all spiked or bolted in place that way. Why they were done this way, I have no clue… If your line is really far backwoodsey, say a logging line, they may well have made guardrails out of timbers. Or maybe had no guardrails at all. There’s bound to be a prototype somewhere for a guardrail-less bridge, Fred’s fixation notwithstanding. (Oh, brother, Oh Father, I’m gonna’ get mail now…!)
Now, if you’re talking about handrails along the walkway, for personnel walking across a wooden trestle or hanging out around the waterbarrel, where your beercan is going to be, then in the 19th c. those guardrails were usually made of wood. I bet there were exceptions, but I’ve never seen any. Metal (pipe) guardrails came into use in the 20th, and that’s what I’d expect to see on non-wood - on steel or concrete bridges.