Are you flying with your pet? Or shipping them alone? Will they be in the cabin, or in cargo?
I've traveled with my pup a few times with AS and definitely prefer them over my experiences with Delta. I've found them to be quite gentle and professional, and if you're traveling with the dog, they've always been good about getting me the "dog on board" note in my seat.
As far as time of year I've never found cold to be a problem. I've flown a dog DEN-FAI in late December, and FAI-GEG in late November, never with an issue.
I know that most airlines have a hot/cold policy, but as Alaska's policy is this:
Pet Embargoes
Customers traveling on Alaska Airlines flights 2000-2999 or flights 3440-3499 may not check pets in the baggage or cargo compartments during the following dates:
November 24, 2014 through December 2, 2014
December 12, 2014 through January 2, 2015
Pets in Cabin will still be accepted during these time periods.
http://www.alaskaair.com/content/tra...with-pets.aspx