I say softshell, David. In my experience, softshells are better suited to ice climbing for two reasons.
First, they’re more breathable than hardshells, a critical feature when you're either working hard and sweating or sitting in a belay. The last thing you want is to get wet. Second, almost by definition, the precipitation you're likely to encounter when ice climbing will be be snow. Softshells are water-resistant in rain, and for all practical purposes they're as good as hardshells in snow.
One problem I've had with the softshell category is defining it. Some makers take a hardshell and give it a lightly insulating lining. To me, a jacket with insulation isn't a softshell. A proper softshell is a garment made from a woven fabric. That fabric may be double-layer, but neither of the layers are fully waterproof and there's no synthetic-fill or down insulation.
Probably the classic softshell for ice climbing is the Arc’Teryx Gamma MX Hoodie ($349 U.S.). It’s a full-featured piece, with an excellent hood, a moderately long cut for good coverage, and chest and sleeve pockets. The outer surface is made from woven nylon and Spandex, and the inner is a light fleece for breathable light insulation.
Patagonia also makes a solid shell for ice climbing called the Northwall Jacket. It’s made from Polartec Power Shield, which is my favorite softshell material. It’s warm, breathable, water-repellent, and tough. Patagonia has bonded the Power Shield to a light fleece lining, making it slightly warmer than the Gamma. I'd choose this jacket if you expect to climb in very cold conditions. It's more expensive at $449, but hey—with the exchange rate in Canada, you'll get a hefty $4 discount, at least at Mountain Equipment Co-op.
If you think you may encounter serious rain on any of your climbing expeditions, I'd recommend checking out the Marmot Zion. It's made from Polartec's three-layer NeoShell material. The Zion is fully waterproof and retails for $379.