A sad commentary when we all try to give advise to a landowner on how to prevent hundreds of dollars worth of damage to their property by spending even more money for fences, the chainsaw to cut down logs, etc.
If the access to your property is in two locations, one on and one off, try putting together 3 or 4 saw horses (a few 2x4's and the sawhorse brackets. Place them at the entrances onto your property across the trail with private property signs on them. The ones at the lake end can be at the bottom and top of the stairs with perhaps some string or construction tape blocking off the stairs. Still money spent, but at least the sawhorses can be used in the summer for construction projects, put a sheet of plywood on them for buffet tables, etc, and a lot easier to put out than rolling logs in place or erecting/taking down snow fencing. I would also get some extra private property signs, attach them to small boards with eyelets on the back, and you can use bungee cords or twine/small rope to attach them to trees to mark your property line in winter, and take the unsightly signs down in the summer (hopefully no four wheelers on the island in the summer
).
Hopefully that will work, be relatively short money, be easy to put out in the fall, and easy to take down in the spring. Sorry for your trouble.