And one eposide Kate told Uncle joe to chop some wood for the stove so she could cook dinner. But how do they get the wood to the the hotel if there's no road?

I too have been watching the show. Haven't seen the show in a long time. Don't recall ever seeing the black and white episodes. I do notice older sister Billie Jo is a make up girl. I wonder if she gets her make up at Sam Druckers. The long eyes lashes I see on Betty Jo too.
One of my favorite episodes is the one where Billie Jo works for the book author who is now an older man and Billie gives the impression he is young. Kate thinks Billie is off to Paris and confronts the author. Billie has good
secretarial skills.

I too have been watching the show. Haven't seen the show in a long time. Don't recall ever seeing the black and white episodes. I do notice older sister Billie Jo is a make up girl. I wonder if she gets her make up at Sam Druckers. The long eyes lashes I see on Betty Jo too.
One of my favorite episodes is the one where Billie Jo works for the book author who is now an older man and Billie gives the impression he is young. Kate thinks Billie is off to Paris and confronts the author. Billie has good
secretarial skills.
Yea the balck and white's are now being seen on MeTV, which are the first 2 years.

And one eposide Kate told Uncle joe to chop some wood for the stove so she could cook dinner. But how do they get the wood to the the hotel if there's no road?

Interesting and fair question, when and where verisimilitude is required: Usually away from sit-coms and fantasies.

Notice that the Shady Rest is in a wooded area. Sick trees nearby could be felled as needed. The farmers in the area could expand their fields, as Mr. Douglass tried in an early episode of Green Acres. They could have got their wood from the same supply source as the Cannonball, which always had a full tender (probably because the real train engine was oil fired, IIRC).

Subject for a fan fic? Maybe some questions just have to be ignored. :-)