Even a few feet will help. Look for a sheltered place to camp , perhaps behind a some bushes or big boulders. Reduce your mileage goals until you are acclimated . So be prepared for the conditions and be flexible enough to change your plans if the going is slower than you expected. Carry a compass and a map showing other trails so that you can bail out if necessary.
Snow often lingers into summer.
If you expect to encounter snowfields, you'll need an ice ax and crampons. Or wait until later in the day, when the ice starts to melt and you can kick in steps. Respect the mountains. They're bigger and stronger than you are. Work Outdoors at GORP Jobs Click Here.