When shipping eggs in cold times, I always let my customer know about the risks and keep attention on how the weather looks between us when the eggs are being shipped. It almost never gets cold here, so I'm used to just simply lots of rain, however the way there or the destination may be very cold.
Insulating the eggs with extra padding can help.
Choosing a decent week can help, and let your customer know the risks of the weather between you and them.
As long as the temps the eggs are exposed to don't fall below 39 degrees, they should be relatively fine.
Most of the time eggs in the winter make it through pretty well. Usually sales drop because of two main reasons -
1) lack of production and
2) lack of want to hatch them at this time. There's so much more involved in raising the chicks and also in making sure the eggs have a safe incubation. You're already using more of your electric bill in the winter, so, eggs then chicks. . . Even more