The three most important items of clothing to get right are:- (1) A pair of boots stiff enough to hold a crampon (minimum B1, depending on your activity) and to kick steps in hard snow. (2) Suitable gloves (warm and waterproof, but also dextrous) – and carry 2 pairs minimum. (3) A full waterproof and windproof ‘shell’ layer – jacket and trousers. This is your first ‘life-saver’ item.
Here is a full kit list of what you might need to wear and carry.