I'm no pro, but I agree with Speed Racer - I would absolutely fence through the creek if there's no other option. Not to mention who knows what the condition of the outside edges of those culverts is like. All things considered (edges of culvert, roadway, steep incline, etc.) it's just safer to prevent an issue before it even occurs.
The idea in AlwaysBehind's post is a good one. Would save post holes being dug underwater but also fence the area in question.
Awkward situation - let us know what you end up doing. Would love to see the finished product.