A lot of that depends on how warm your core is.
Yes, it is possible to go down to freezing and slightly below. Sometimes it as cold at 50F/10C.
Open hard rocky ground and strong winds at some altitude is very different from heavily forested areas at 1500'/500M with no wind. Climbing a steep slope is different from a long slow descent.
Anyway, a good set of trail shoes and shorts can handle cooler weather down to about 40-50F if you are activly working, ie climbing, hiking in little wind. Water doesn't matter because you will likely be sweating, anyway. Keeping your core plenty warm means your body will be pumping blood to your arms and legs (feet and hands), so, you should be OK.
Stopping will become a problem. The minute you stop, at lower temps, you will get chilled. Then your hands and feet will start getting cold, because your body constricts blood flow to your extremities. Adding layers over your core will not help a lot without also walking (to warm your legs and feet.) Wet, will only exacerbate the problem. Leaving you in a bad way after 15-30 minutes. You need to get dry and add layers to your legs and feet. But, that wasn't what you were asking... Anyway, keep the additional layers dry in your pack. Set up a roof (tent or tarp) immediatly. Change into dry cloths and eat/drink something warm as soon as you can. We call that hypothermia weather in the ADK's. Good for hiking...but difficult to stop. If you don't stop, exhaustion can quickly set in.