Mittens are generally out, except for donning at cold belays. How you dress is almost as important as what you wear. The theme here is low bulk. Tuck your jacket and jacket shell under your harness so you can easily access racking loops. Likewise, wear close-fitting gaiters over your fleece or shell pants to keep your pant cuffs out of the way of hungry front points.
Some climbers carry light and versatile hexes in place of heavier cams.
RPs and TCUs are useful on climbs with clean, dry cracks. Tri-cams work in shallow holes where nothing else will stick. Your belay device should likewise be ice-proof. Straightforward cragging or toprope sessions are best done with a single 10- or 11mm rope of the same caliber you'd use for regular rock or sport climbing. Then slip on rock shoes and a helmet, and hook around.