My son saw a pest control commercial this morning and asked “Did Abraham Lincoln have termites?”
Was that a common occurence in log cabins, or did they use pitch or something like that to prevent / control termite damage?
Don’t know the answer to the OP, but a more interesting ad might be “Did George Washington have termites?” 
I’m not sure why you sinmgle out Log Cabins – most colonial and early American buildings were constructed of wood. If you Google “termites” and “Plimouth Plantation” (or “Old Sturrbridge Village”, or “Colonial Williamsburg”, or any other such site) you’ll fuind plenty of casual references to termite damage, but nothing at length. Nowadays, jusging from these sites, they use various protections and sprays. They used to use creosote. But I don’t see anything about any contemporary remedies.
In my homer town, what was the library (and is now a history museum) started out as an early 19th century church. Around the time I was born the floor was extensively damaged by termites, and they pulled out the infested timbers and replaced them. I expect that’s what happened in Lincoln’s time.
I should point out that termites don’t attack every building, and some woods are more resistant. There are plenty of colonial-era buildings without termite (or other insect) damage. And some places are worse trhan others. The first time I flew into San Francisco, I was amazed at the number of termite exterminator ads I saw ion the taxi ride to my hotel. I gather that the Bay Area is a hotbed of termite activity./
Tom Lincoln, Abe’s dad, generally didn’t stay in one place long enough to worry about termites but lived in his last log home for 30 years. During that time he may have needed to perform some maintenence due to termite damage but in general he was no Bob Villa.