Day trip north-west peak on Mt. Huashan in mid January

Hi, I'm going to visit the mountain for a day trip from Xian in mid jan next year. My plan will be to take a cable car to north peak then hike to the west peak and take the cable car down. My question is how long would it take to get to west peak from north? Will it be too cold and slippery to hike then? (especially with the heaven's ladder and dragon's ridge). Thanks!