My whole family will be staying at E Joy aparment in Xian city center on the 20/12/2015.

There is no direct transport mode. You are suggested to take a taxi, and the fare is about CNY50.
If wanting a cheaper way, you need to transfer buses: near the apartment, you can walk to Huangyancun bus stop to take the bus No. 706 or 608 to Zhuquemen (Xiaonanmen). And then right at the bus stop to take the bus No. 910 to Hangkong Lvyou Xueyuan. Then walk about 300 yards, you will reach the ski resort.

Thank you very much for the advice. I appreciate it if you could recommend similar resorts nearby and how to go over there.

I experienced a lot of fun at Cuihua Mountain Ski Resort, but it is much farther than Bailuyuan Ski Resort, which actually is the nearest one to your apartment. It is equipped with sound snow making machines. Moreover, there are various trails for intermediate skiers and beginners. Have a try!