I’ve never been on the Cog. We always drove up the Mt. Washington Auto Road. To me, that’s the only way to go up. If you go up in the fall, make sure you have extra warm clothes. Even in the summer it can get pretty cold up there.
We tried to do this but it was cold and icy and we were told we could only go so far which we did. The wind was awful and when I opened the door it whipped it away and it hit the car next to us. Steve was very impressed.... not. We did exchange details with the guy and as it was a hire car we were not too worried as we had insurance.
I could not believe how cold it was up there though. Brrrr.
We drove on a road called the Kancamagus Pass - US112 - which was really pretty for the trees, this is in NH. I cannot remember the whole road but
think it was OK for an RV, in fact looking at Streetview the Google car was following a small RV. There was a covered bridge, I think the photo from Chet shows it, but this was off to the side if I recall correctly.
Check your route carefully to avoid those covered bridges which are very pretty to see but you don't want to come across them and end up holding up traffic or worse!
We also stayed in the town of Inlet which is still in NY and it was really lovely at that time of year with the fall colours. I think if you go anywhere with a forest with the right type of trees you won't fail.
Hope it all works out for you.