Bill,
We are fortunate here in that there are several restored cabins in all directions within 50 miles of where I live. Most of them date around mid 1830's to 1860's. One south of here is even a restored 2 story cabin. From what I read in the Foxfire books and a few other books along with what I've seen. Construction techniques on most simple one room cabins hasn't changed that much over time. That is until modern power tools were starting to be used.
Books on log cabin construction, both of the history and architectural plans are commonly available through new and used book dealers. It seems during the 70's and early 80's there was big interest in log homes and everybody was publishing a book on the subject or to some aspect of log cabin construction. Could have been The Foxfire books had something to do with igniting the interest, I don't know. The foxfire book 1 and 9 gives the basics on cabin construction, foxfire 3 talks about building a smokehouse. Another good book on cabin styles from very early to modern revivals is Alex Bealers book "The Log Cabin" 2nd Prnt 1978. Dale Mann's book "the complete Log House Book" also covers the basics on the different aspects of log construction. There is a lot of info available on cabin construction. A person could build them as rough looking or as pretty as you want, it just depends on the purpose and the amount of time you wanted to invest in one. Most construction methods and plans that I have seen on one room cabins are usually very simple and very similar and would be correct even for the early 19th century. In the end there's only so many ways you can stack those logs and raise the rafters.
Smokeydays