I've pulled irrigation pipe through worse.
They will pick the easiest path without large trees if possible, the blade on the back of the machine will easily cut through most near the surface ( 6"-12" ) roots. They will shoot the cable in, the cable spool is mounted on the back top of the machine and it's feeds into the ground through a slot in the back of the blade. If the roots are bad they will cheat and pull the cable close to surface. Is the nearest cable box on the other side of the woods?
If it's a subcontractor they get paid to bury per foot of cable and certain amount to for things like boring under sidewalks, roads and driveways. They will go the easiest and fastest route.
I would suggest taking pictures of your driveway before they get there and make sure they are dated or email them to yourself. If your driveway is asphalt and they don't dig deep enough on each side and bore it's easy to put a hump in your driveway. And almost impossible to make it go away. Basically a bore is shot under your driveway with 8'-10' rods the connect together and the drilling end will have a bit at least 1" or larger. The other end connects to the plow and it sounds the boring rod and the operator moves the machine forward to drill and backwards to remove the bit from a open trench dug on each side of the driveway.
You should know they are coming soon because your underground utilities have been marked.