Will it be snowing in late Dec in Shenyang?

Hi, it is hard to tell whether it will snow then this year. But according to the past weather records, it might have snow.
As for your case, I suggest you go to the local clothing wholesale market to get what you want. Wu'ai Clothing Wholesale Market is suggested. Bus No. 103 and 219 can take you there directly.
The Ski Resorts is not needed to be booked in advance. For the advantaged condition and service, you can go there and buy the ticket to enjoy yourself directly.
Regards!

But how to get to the Ski Resorts from the airport? Is it far?
Which Ski Resorts you can recommend?

Northeast Asia ski resort and Baiqingzhai Ski Resort are suggested.
It is a little farther to the former one from the airport. While as for the latter one, you can take airport shuttle bus to the local TV station first. Then you need walk to Wencui Road, Color-TV Center to take bus no. 166 to Hetai Dongfangyuan. After that, you have to take bus no. 387 to baiqing Station, from which station you can walk to the ski resort.