60 degrees -50 degrees
Boxers can get used to many diffferent climates, if you expose them to many different ones as a pup they won't be as scared or dislike the climate when they are older.
I also live in Idaho and with the snow right now my 12 week old boxer loves to run around and jump in it. Usually after about 15min though she is ready to come back in. We got her a sweater and with that she we stay out a little longer sometimes. The first time it snowed she didn't want to go outside but it just takes a little getting used to.
**My family and as my father grew up, all in Idaho, owned boxers. You would really need to be sensitive and thoughtful to the weather conditions all year round. Every night and most days in the winter (and potentially at any other time), the dogs would pal around inside. We had nearly an acre of lawn and we'd let them out in the winter for a spell during the day to play in the snow. Their breed personalities are at full swing. They LOVED that!! Often times with a sweater for them 'even at their size.' But once (like people) the shivers set in or they look at you with those big brown eyes, it's time to go back in side to play with a family member and wind down a bit. Our family therapy was our beloved boxer pets! Ours happened to be very frightened of lightning and Idaho wind storms, so those were other occasions to consider. You'll learn to be in tune with the outdoors in a new way, just don't drop the ball. Other Idaho owners have let their boxers die mistakenly in a (cold) unattached garage, etc.
Boxers are tough, but they have thin skin and short hair. If it's cold for you, chances are they are cold too. If winters are harsh where you live, I would suggest getting a jacket for your boxer and perhaps some shoes/booties for the snow. Your dog may not like to wear the jacket and boots at first, but starting him/her with wearing them for a few minutes a couple times a day around the house, and with positive reinforcement, they will get used to it, and you will be able to increase the time they will wear it.