Due to its location, Istanbul is close to nearly everything. You can do day trip to many places around Istanbul, as well as two snow skiing resorts.
The closest one is Kartepe formerly known as Keltepe is in the south east of Kocaeli-Izmit province and only one and a half hour away from Istanbul. Kartepe Ski Centre is located at an altitude of 1650m on Mount Kartepe which is covered with a forest consisting of hazelnut,oak and chestnut trees.
In Kartepe Ski Center there are 4 lifts, 3 chair-lifts and 1 teleski. The length of the tracks is from 400m to 3500m. Between late December and late February, is a good period for skiing and snow thickness is between 80 and 200 cm.
Apart from snow skiing you can also do some other things at Kartepe. You can do snow board or you can hire a sled and have fun.
The villages at the bottom of Mount Kartepe are also nice and interesting. You can visit those villages, meet some villagers, have a traditional turkish tea with the villagers and then drive up to ski center to enjoy snow.
The second ski center close to Istanbul is Uludag. Mount Uludag is the highest mountain of Marmara region and 2543m.. The park where ski center is 22 kms away from city of Bursa and Bursa is 3 and a half hours away from Istanbul. The park can be reached by driving or cable car from Bursa. The cable car goes first to plateau of Kadiyayla which is at 1200m and then ends at plateau of Sarıalan which has an altitude of 1630m.
In Uludag Ski Center there are 8 chair-lifts and 7 teleskis with a capacity of 1000 person per hour and 13 various ski tracks which are about 20km long.
The best time for Uludag is from second half of december till end of March and in normal winter conditions snow thickness can reach to 3m.
You can enjoy the view while you are ascending by cable car, do snow skiing, hire a sled or just sit at one of the cafes availabe there and enjoy your hot drink while watching the white beauty.
Daily tours available from Sultanahmet to both ski centers. If you check with your hotel, they will help you to make arrangemenet to do daily trips to those places and come back in the evening to your warm hotel room.