The logs on log homes nowadays are usually double tongue and groove with gaskets between each layer. So the infiltration issue you mentioned should not occure. I am just talking in theory here since I have never lived in a log home or known anyone who ownes one.
I could imagine the house you and your father built years ago was very drafty just looking at the gaps between the logs.

If you like the look of a log home you could veneer half logs to the exterior walls (like siding) this way you can frame your house conventionally and then apply the logs just for looks. And if they fail (rot) just replace them like you would with siding. Of course you would not get the cabin look you might want inside the house. But on the outside you would never be able to tell.
Or build a TF with SIPs or whatever you feel comfortable with as enclosure and instead of siding you apply the logs. So you get a TF home where you can admire the joinery and the cabin look on the outside. Best of both worlds .