Anyone ever run a line just setting culverts or streams very close to roads for rats/otter/mink in the winter? For ease of being able to check fast after or before work? Worth it?

Sure you can, it’s a common practice. Heck, a fella near me sells a video “Gary Schumann’s Rat Race”. The real question is, is it worth it? That’s for you to try it on for size and decide if it fits! Big difference in fur $$ from when Gary made the video in 2010 and now!!!

I did it for 30 years. But now you have to have permission at every culvert on the road system. And getting permission from the state or county isn't going to happen. So, I don't think you can make it work.

Even if it's public land?

In some cases, you would be Ok. But you better check on those locations. Some have trap restrictions.
I trapped some public land and had no idea that you could only use DPs on some sections and in other areas you could use foot holds.

Here in Maine did it for years but in the fall.Couple years catching over 100 mink.All blind seta

I could see it working well in Maine, I have hunted, fished, and ridden snowmobile in the County and the amount of road systems with culverts and vast area surrounding it all would be heaven to trap this way.

Permission and number of stops is all that is really needed. I remember a story in the Trapper years ago about a guy driving a beat up car doing it, he carried all his gear in a bucket, and would raise his hood at every stop so it looked like car trouble, people passing by wouldn't pay him any notice.

Did that for the first ten years I trapped. Targets were nutria #1, coons and beaver. Goal was always $100/day. Gas was .65 cent/gal on avg.

I was doing nuisance beaver work On the railroad in the James Bay lowlands north of Otter Rapids one fall.
I set 36 beaver traps on superstands all in culverts,I let them soak 2 days and picked up 32 beaver one muskrat and one otter first check.
Easiest trapping ever.

Per the current Wisconsin regs:

This would be regarding just roadside setting though wouldn't it? I'm planning on setting culverts that are public land on both sides of the waterway making it legal

Not only getting permission people need to get but every trap thief out there won't have to travel very far to grab your equipment.

Trapping woods roads up here in northern Maine no permission needed.

I set culverts sometimes, but only if I know it's going to stay open, same with bridge crossings. People around here tend to avoid water in the winter, but once it freezes good it becomes an access point and then everyone and their sister is riding a snow machine up and down the creek past your stuff. Our creeks turn into highways once they'll support a snow go.

The only people doing that here in Maine in the winter time would be beaver trappers.

I getting ready to start a relatively short creek bridge line for mink & otter myself as soon as I have safe ice. BE mink sets really shine under ice in culverts & concrete bridges AND the trap thieves need to be bringing a frigin spud with them in order to steal my catches & traps! Sure, I had to obtain permissions from the property owners who own to the centerline of the roads & bridges but what’s the big deal with doing that?
So much to trap and so little time!

Here it's everyone and anyone. Other trappers, snow machiners, mushers, x country skiers, and people on snow shoes. A guy has to cover a lot of ground, enjoy bush whacking, or run some sketchy ice to get away from the masses

Thankfully, we can trap the R.O.W. here in Iowa. Can't imagine having to run down permission for every bridge and culvert I set.
But to the OP's question, yes it is worth doing and is a great way to catch a lot of fur.

I went to high school with Gary, he was a year ahead of me. He was a trapping machine back then too!!!!!

Here in NY if you are trapping state or county land you are good to go. But if there is private property involved you need permission.