Hello, it sounds like you and your friends have a great trip ahead, I love the Whites!
My first questions are about your dogs: How old are they?, What breed are they?, do they live mostly indoors or outdoors?, and are they emotionally dependent on you?
Young and older dogs (just like us) will have greater difficulty moderating their temperature and combined physical effort required for the White mountains.
Some breeds are better suited for the weather/seasons then others. For mixed breeds, this is mostly evident if they have both fur and guard hair and how thick/bushy their coat is (including tails and ears).
Living outside or spending a large portion of their time (regardless of the season) is good for dogs traveling outdoors in many ways, most prominently in cold temperatures, it allows them to shed their summer coat for a thinker winter coat.
Emotional dependence is more of a comfort for the dog. Is the dog comfortable being left outside by itself for the night (regardless of weather/temperature) or do they require constant companionship from you or other dogs?
The answer to these questions will offer insight into how well your dog would be suited into being outside in your desired season, weather, and camping situation. Your dogs may need nothing except a leash to keep them from wondering off at night after something interesting or a nice sleeping situation that Racheil posted for you.
If you feel you need to augment your dog’s comfort with gear, you will find there is as much gear for them as there is for us!
I hope you all have an awesome adventureI