JRinGeorgia is right, temp isn't the issue, it's the density/composition of the atmosphere and how much UV is absobed there before it hits you, and at higher altitudes the UV exposure is greater. I have allergies to a number of the chemical sunscreens/blockers so have been using Zinc Oxide and Titanium Dioxide formulas since the get-go almost 2 decades ago. So far, so good, knock on wood.
Right now I'm using
KissMyFace's Natural Mineral Sunscreen SPF40 which can be had at REI among other places. 10% zinc oxide, 6% titanium dioxide. Both non-nano particle size.
If I am concerned about wind-chapping, I'll use a formula with lower water content. I used to use Dermatone's Titanium Dioxide blend* and though heavy, once on, if I didn't rub it off with my hankie, it stayed on all day. The KMF is working pretty well. If I need more wind-chapping protection, I'll use one of Badger's 18-22% zinc oxide blends. I like the Lavender scented one. The "unscented" just smells like oil to me. The two Badger's I use are heavier, but work, and prevent chapping.
I usually have my chest covered, but my neck gets indirect UV. I use
Kinesys SPF30 Fragrance Free spray for that, since it's not tacky and doesn't feel ikky.
With a physical blocker, you only need to reapply if you rub it off. Chemical sunscreens wear out and need reapplication, and need time to absorb before they are working at full effectiveness. As soon as you apply a physical blocker, you are protected.
I have a number of friends who did not protect their skin over the years and the sun damage is obvious. Deep lines, some have had melanomas, there's a genetic component, obviously to all this, and YMMV, but I do what I can to tilt the odds in my favor.
Wear a hat (with cape or bandanna around your neck) to protect ears and neck and wear good sunglasses. Long bills with black underneath reduce direct and indirect rays. We use glacier glasses with pouches around the eyes to really seal out reflected rays. Sunscreen only goes on exposed skin under the glacier glasses, so we don't need much.
We wear fingerless gloves and even though we put sunscreen on our exposed fingers, you can see the difference.
UV at altitude is no joke, and we spend as much time as possible at 10,000' or higher, so we don't mess around. We see plenty of folks with tanks, shorts and the like. If you know what you are doing and prefer that option, fine, your skin, your choice. But if you don't know how much UV you can handle (and only time will answer that), protect yourself.
Also, polyester is naturally UV resistant, nylon is not. Nylon products that say they have UV protection usually have a coating from the factory that will wash out over time.
*Dermatone got sold, stopped making my favorite tin of goo... Turns out if they were using nano-particles (which I hope they didn't - it was obviously white when on), this could be a bad thing... Search on nano-particle sunblock and you'll see why. So who knows. I'm now more careful reading the labels...
Good luck and have a great trip!
More sunscreen info