Generally speaking, mid-January is a good time to see the sculptures. About skiing, you can go anytime from December to next march. You may have a look about the schedule of 2011 Harbin Ice and Snow Festival by clicking the link listed on the top of this page, so could decide a departure date to attend your prefered activities. From Singapore to Harbin by plane? I'm not sure, seems the flights by China Eastern Airlines are cheap. You may serch by yourself at Cheap China Flights(https://www.travelchinaguide.com/china-flights/) .