A 12" border of plant material like Vinca, Euonymus or some low ground cover that is green year round, that doesn't mind being plowed up and comes back. Then fill in with wood chips - they deter grass growth while the ground cover takes hold. You can mow the vinca or other low plants back as they start to engage the lawn.
As pine states you can define it with Hydrangeas, - good if you dont have trees or leaves to clean up and these are 2-3' high or Forsythia, but these get 10-12' high and are a PIA to eradicate and require annual pruning to stay small - plus these will impede your snow plowing / pushing ability off the drive.
Curbing with PT wood or stone works too, but since youre in a snow zone this has its issues. I installed used granite curbing 4" Wide x 12" Deep x length and 1" or 2 above ground so 10" deep and you know when the bucket or blade hits it under the snow. Its relatively cheap here in NH as it comes in pieces from recon jobs in 2-3' sections.