The temperatures in December aren't quite as cold as in January, but there's not very much difference. The average high in Namche Bazaar is 44°F (7°C) this month, and the low hovers at 21°F (-6°C). As Namche is 'only' at 11,290 feet (3,440 meters), temperatures higher up will be much colder.
Rainfall is still low, but not as low as in November, and you may encounter snow anywhere along the Everest Base Camp (EBC) trail, not just at higher altitudes. You're very likely to enjoy some beautifully crisp and clear mountain views in December.
Crowds & Costs
After the busy months of October and November, the crowds start to thin out in December. Some teahouses close for the winter, with their owners migrating to Kathmandu. But, you won't have trouble securing a bed at the places that do stay open.
If you're prepared for cold temperatures, especially at night, and are aware that you might have to turn back at any point if there's too much snow, you can embark on the classic EBC trek this month.
As temperatures are cold in December and snowfall can be a problem, it's best to avoid alternative routes in the Everest region that require crossing high passes (such as the Three Passes Trek). Treks that stay below 13,000 feet will be safer and more comfortable, but it's essential to check (or have your guide check) the weather conditions as you progress along any trek in this area.
To avoid the coldest conditions, try a shorter trek in the Everest region that doesn't go all the way to EBC. Basing yourself in Namche Bazaar is a comfortable option. The town is a two-day walk from Lukla, and there are many good day hikes in the area. You won't see EBC itself from there, but you can enjoy some pretty spectacular views of the region.
Another option is to take the 'Pioneers' Route' from Jiri to Lukla, which is the trail that early mountaineers took to access the Everest region before the airport was built at Lukla in the 1960s. Jiri is a day's drive from Kathmandu. Or, fly from Kathmandu to Phaplu and trek through the Solukhumbu region from there. These trails are rarely trekked these days, and provide a gradual (though not necessarily easy!) approach to Lukla and the Everest region.
December is also an ideal time to consider treating yourself to a luxury tour—there are some lovely luxury lodges in the Everest region (such as Yeti Mountain Homes and Everest Summit Lodges) on a par with comfortable boutique accommodations in Kathmandu. While this kind of trip is special at any time of year, it's even more so in winter, when you'll especially enjoy the comfort of a warm, cozy lodge at the end of a day of walking.
What to Bring
It's important to be well prepared for the cold in December, for your safety as well as comfort. Although many teahouses provide blankets, these won't necessarily be adequate for winter conditions. A winter-weight sleeping bag is ideal. Also, bring a warm down jacket, ideal for its light weight. Warm clothes for the evenings and nights are also essential, as well as good woolen hats, gloves, socks, and scarves.
Sunscreen is also essential, as the sun is strong in the mountains, even in December. It's best to bring this from home, as varieties are limited in Kathmandu.
Almost all other winter equipment can be bought or rented at trekking shops in Kathmandu, in case you don't have your own winter trekking gear and don't need it at home.
Getting There & Away
The quickest way of getting to the Everest region is to fly from Kathmandu to Lukla. While rain is less likely to cause delays and cancellations in December than in some other months, it's still possible. Plus, Kathmandu experiences some fog in the winter, which has the potential to disrupt flights to or from Lukla, even if the conditions in Lukla are good.
Alternatively, trek the whole way from Jiri or Phaplu, as mentioned above.
Events in December
Tamu Lhosar is often celebrated in December (Hindu and Buddhist festivals follow a lunar calendar, meaning that a festival held in December one year may be in January the next). Lhosar is the name for Tibetan Buddhist New Year, but different ethnic groups in Nepal celebrate different Lhosar festivals, some as late as February. Tamu Lhosar is celebrated by Gurung, Magar, and Tamang people, and is a lively event in Kathmandu.
And, of course, a trek in the Everest region is a memorable way to spend New Year's Eve. To experience Himalayan nightlife, aim to be in Namche Bazaar on December 31. There are bars and restaurants in the little town—just remember that the effects of alcohol tend to hit harder and more quickly at altitude, and you wouldn't want to write off your January 1st.