While you may wish to leave the logs exposed for aesthetic reasons, there is no reason to leave them exposed to save energy. Log cabins are not particularly energy efficient.
- Though manufacturers claim they are energy efficient because of the thermal mass, this mass is made of wood, and wood isn't a very good thermal mass.
- Thermal mass stores the temperature gathered in the day and releases it at night, and vice versa, resulting in a more even temperature.
- Good thermal mass materials are concrete, stone and water.
Ideally add exterior insulation
Ideally, a layer of insulation on the outside of the building would help hold this temperature and south facing glass would help gain it.
But since you have a nice log cabin, you probably don't want to cover the outside walls with insulation.
Adding insulation inside
Insulation and drywall on the inside is a very good suggestion.
An open cell foam would continue to allow the wall to breath, and that could help to avoid any condensation occurring from the difference between inside and outside temperatures.A building paper between the logs and the insulation might also be a good idea.
Since the logs themselves will create many voids because of their shape, another solution would be to allow an airspace between the logs and an insulated panel, such as EPS rigid insulation sandwiched on drywall on the interior, with some ventilation between, so there is no moisture build up.
These solutions do not rely on the wood's thermal qualities, but on the quality of the insulation you use.
In the long run, that's a better bet.
For more information:
Read "I have a log home. Will insulating my interior walls lower my electric bill?" a Q&A answered by Harold Remlinger.
Also, read "What is the value of log construction to meet energy efficiency or other green standards? The logs would be locally sourced." a Q&A answered by Polly Osborne.