Dealing with dry nose/throat when flying

I think everyone has that problem. Try saline nose spray. A damp towel, flu mask or other cloth over your mouth also helps.

The two existing answers are fine (I already carry an empty water bottle, and I shall certainly try the wet towel on my next journey) but to help clarify the source of the dryness, I quote (without permission, on a fair-use basis) from Patrick Smith's "Cockpit Confidential: Everything you need to know about air travel" (Sourcebooks, 2013).

If passengers have one very legitimate gripe, it's about dryness. Indeed, the cabin air is exceptionally dry and dehydrating. At around 12% humidity, it's drier than you will find in most deserts. This is chiefly a by-product of cruising at high altitudes, where moisture content is somewhere between low and non-existent. Humidifying a cabin would seem simple and sensible solution, but it's avoided for different reasons: First to amply humidify a jetliner would take large quantities of water, which is heavy and therefore expensive to carry. Humidifying systems would need to recapture and recirculate as much water as possible, making them expensive and complicated. They do exist: one sells for more than $100,000 per unit and increases humidity by only a small margin. There's also the important issue of corrosion. Dampness and condensation leeching into the guts of an aircraft can be damaging.

The Boeing 787 has the healthiest air of any commercial plane, thanks to filters with an efficiency of 99.97%. Humidity, too, is substantially higher. The plane's all-composite structure is less susceptible to condensation, and a unique circulation system pumps dry air through the lining between the cabin walls and exterior skin.

Continue with the greater-than-normal drinking, but make sure what you are drinking is not alcoholic.

One tip for making this easier is to bring an empty water bottle with you and then fill it once you've passed through security. This will allow you to stay much more hydrated that relying on the slightly-larger-than-thimble-sized cups typically provided to passengers in economy. Many countries won't allow you to bring a water bottle that has liquid in it through security, but you can typically bring an empty one and fill it up prior to boarding. At least in the U.S., drinking water fountains and even dedicated fountains for filling water bottles are common in passenger terminals. In places where this is not common, you could possibly ask one of the airside restaurants to fill it with drinking water for you.

Of course, another option is to simply buy a bottle of water or other non-alcoholic beverage in the terminal after passing through security, but this option is obviously more expensive. Note also that there are some flights where neither of these options will work and any water bottles with liquid in them are confiscated or emptied immediately prior to boarding the aircraft. These are more the exception than the rule, but it happens on some routes such as China to the U.S. or Australia.

Another factor that can make a difference is what type of aircraft you're flying on. Newer aircraft like the Boeing 787 and the Airbus A350 have higher cabin air pressure and humidity than most older aircraft designs. If you're able to choose flights on those aircraft, the dehydration effect should be considerably less, though still present to some degree.