It is not ice in his hands, Its his Valyrian Sword "Longclaw" Covered with ice.



I don't think he is a white walker, as his eyes are not blue.



Second, Night's kings power is to raise dead to life as his Undead servents & those are called "Wights"



So either way it goes Jon Snow is not depicted as So called "White Wallker" in this art.



PS: For Now as per show this theory doesnot matters anymore.



But ARTWORK IS EXCELLENT.