>>890399My cyclocross bike is great for snow, but I'd want clearance for more than 35mm tires (becase Schwalbe Marathon Cross 37s are a good snow tire, and because I want room so the snow doesn't pack up under my fenders - and in the winter I definitely want fenders). 35 should do the job though.
Studded tires are really good on ice, in the city I usually only use one on the front (it's all you need to stay upright). I only use both if it's really icy or I'm riding on the frozen harbour or something like that.
Road handlebars will help you get more aerodynamic but it's really a matter of preference and comfort. If you want to be speedy in the summer fast tires will make a big difference. I like road handlebars for most riding other than mountain biking, but flat bars do give you more control in the snow.