The question is: are steel grate bridges actually dangerous, or am I just paranoid?

One leg of my ride to the train station gives me the choice between a half mile along the towpath of the Delaware and Raritan Canal, or a mile of rather rural roads, on which there is little traffic but the few cars go too fast. I usually take the canal; scenic and quiet, and gives me interesting wildlife stories to tell elsewhere on this forum. But now we're getting to the mud season. Last week we had snow, which froze to a rutted mess, which thawed to rutted mud over the weekend, and now it has two inches of fresh snow on it. So the road becomes attractive. The problem is the road goes over a small bridge, which is a steel grate. It's one lane wide, and no more than 20 feet long, but my tires slide all over the place on it, especially when I ride my folding bike with its 16" wheels. That bridge scares me, especially when it's wet; I slide around, and it feels like I'm going to fall. I never have, but I hate it with a passion bordering on paranoia.

What do you think, are my fears justified?

Edit, now that I'm going that way, I see I underestimated. That bridge is more like 40 or 50 feet long. Nasty.