My information comes from the log home builders association. I attended their log home building
class and as far as education goes it is second only to my
PDC. I have not built a log structure yet so my
answer is not based on personal
experience but rather what was taught in the class by teachers with 30 plus years of experience building with logs.
Observing the growth rings of trees, the light ring is spring/summer growth where sap is flowing heavily. The light ring is made of soft spongy wood that easily moves water and nutrients through it. The dark ring is fall/winter growth with little or no sap flow, the tree is dormant. The tree hardens off in fall to prepare for winter freezing temperatures and as a result the dark ring is made of very hard, dry wood with higher resin content. In the class it was highly recommended to use winter cut logs whenever possible because that meant that the outer most ring, just below the bark, was the dark growth ring and the resulting log would be more resistant to rot and insect damage. It was also highly recommended that you peel logs using a spud instead of a draw knife because the draw knife's sharp edge was more likely to cut through the cambium layer and into the wood, right through your dark ring, and defeat the purpose of using the winter cut log.
When using spring cut logs the bark peels off very easily due to the heavy sap flow just beneath the bark. However the resulting log has the soft, spongy wood as its outer most layer. There is also more water present in the tree during this active growth cycle. Peeling winter cut logs is much harder as the bark is glued to the wood by that hard, dark growth ring. All that said, I'm positive there have been thousands, if not millions, of buildings built with spring cut logs that are just fine, especially if the building and roof design keep water off of the logs. If you are going to mill the logs at all then you'll be cutting through that outer most layer anyway, use spring cut logs since they are easier to peel.
Now that you have the full picture you can make an educated decision based upon your needs and intended final use of the wood.