I'm hoping to climb Huashan in the middle of March, will it be very cold and icy at that time ?

Generally, yes. It will be cold then. The average temperature at that time will be around 8C. On the mountain, the temperature can be lower, sometimes below zero centigrade.
If you intend to climb then, warm clothes are suggested to be taken. Besides, a pair of skid-proof sneakers of good quality is necessary.