Yes, the road right of way on your private property is open for trapping unless you post it or tell each and every person who tries to trap there that they may not trap there.
Some trappers like trapping in ditches: they can be productive wildlife habitat, and they're easy to drive by to check the traps (many miles for each trapper).
Please spread the word: few dog owners know this, and a number of trappers take advantage of it. Dog owners are often horrified to find deadly traps in the ditch at the end of their own driveways, or along their own roads where they walk their dogs. People don't usually find these traps--their dogs do, and are often injured or killed by them.
Here are a couple of excerpts from the Minnesota Hunting & Trapping Regulations Handbook 2011:
Definitions and Posting Requirements (p. 7).
To be legally posted, land must have signs:
An unauthorized person may not post land with signs prohibiting outdoor recreation or trespass.
Road right-of-way (p. 9).
Some road right-of-ways are not owned by a unit of government. In these instances the landowner has granted an easement for vehicle and foot travel. The landowner generally retains authority to restrict
access for hunting or trapping and may prohibit trespass by posting the land or by verbally directing hunters and trappers to leave the easement. It’s always best to ask permission if in doubt about the ownership of a road ditch area. County or township offices also may be able to help determine the ownership status of a road ditch.