Since Christmas season is packed with tourists, i would suggest you to book your hotel in advance.
Even a single bed will make you drain a lot of money, here are some suggestions for hotels: 1) Himalaya
2) Alka 3) Vikram vintage
these hotels are quite expensive.
Top 5 budget hotels are 1) Tourist Rest house (TRH) there are 2 TRH in the lake city which i guess might be left with few rooms.
2) Lake view 3)Payal
4)Welcome park( preferred).
5) Ayar Jungle camp for further details ..feel free to ask..✌