Patagonia's Core Skin Jacket ($250; www.patagonia.com) is a nice-looking garment, slotting neatly into the soft-shell ideal of "one jacket for 90 percent of the weather conditions most people face." To that end, it has a breathable Polartec outer shell with Patagonia's water-shedding Deluge coating, meaning it will keep you dry for several hours in mist or drizzle, for maybe 30 to 40 minutes in hard rain. And it has a lightly insulated lining that uses Polartec's estimable Power Dry material.
A lot depends on the temps in which you're working out and your own body's reaction to cold, but I should think the Core Skin would work well for most of the activities you mention. Maybe a little warm for running, but very good for cold-weather bicycling (I wear something similar on winter rides) and great for cross-country skiing. My only hesitation would be for downhill skiing, when you're apt to have longish inactive periods waiting in lift lines and riding lifts. But, that could be offset by adding underlayers. The Core Jacket is cut pretty trim, but you could add at least two long underwear layers, such as Patagonia's Capilene Silkweight Mock T ($37) and maybe even a Capilene Expedition Weight Zip-T ($69). Or, certainly Oakley's Summit Top ($50; www.oakley.com), made with Power Dry, will fit the bill.
But, when all's said and done, you have my blessing to go ahead and get the Core Skin. Then get out there and enjoy the winter!