You definitely want it in writing.  Maybe even get a bond.  If they are asking for permission, it's because they know they do not already have any legal right.  Take lots of pictures before they start, so you can prove if they do a proper job of restoring it.  You might ask if they can tell you where there is another road where they have had a similar agreement so you can go and look at it and ask the people there if they were satisfied with the restoration.  And I sincerely hope they do not plan to start work until after mud season - not just when "Heavy Loads Limited" postings come down off of public roads, but when your road is actually completely thawed, settled, and firmed up - which may be quite a while after public roads are ready to support heavy loads, especially if your road is shaded, or if it doesn't have a sufficient base.  One thing to take note of in your before and after assessment - go out when it's raining and note if the road has a good crown so the water sheets off to the sides, or if it has subtle depressions where the tire tracks are, so that water runs down the road instead of off to the sides.  Or go out at night, when your headlamps will accentuate the contour of the road.  I'll attach photos to show how heavy loads can depress the tire tracks, even when the road is dry and firm.  (This can happen even if the road is paved.  If you don't believe me, go look at Minot Ave in Auburn, going northbound, approaching Court Street.)