Acute Mountain Sickness, or altitude sickness, is a very real possibility because of the high altitude in the Ladakhi Range. Leh itself stands at 3500 meters. Early symptoms include listlessness, headaches, and nausea.
The only therapy is to acclimatize yourself. Have very low ambitions of what you want to do the first days. Spend at least three days in the town to acclimatize before venturing out on any trek (many use this time to tour the monasteries/palaces). Don't be goaded into a rushed itinerary.
Drink a lot of water. A good rule of thumb is to drink three liters of water a day and an additional liter for every 1000 meters you elevate. So, your first day in Leh, five liters is the minimum you should drink everyday to stay fit & fine.
Extreme Sunshine and Cold
It may be cold, but the sunshine is still very strong so do as the Ladakhis do and wear a cap! The altitude ensures that sunrays are much stronger than on the Indian plains. Add sun protection cream to your nose, neck, and ears in particular. Places like Drass are among the coldest spots in Asia. Temperatures are capable of dipping to minus 50 degrees Celcius. Dress and plan accordingly for extreme conditions