I rode my Bike Friday Tikit as my winter bike for 2 or 3 Calgary winters. I just used the stock Schwalbe Marathons and it had fenders on it. Studded tires are nice if you have to ride on freezing rain days and for the odd thaw/freeze day, but I didn't find them necessary most of the time. I understand Schwalbe does make 20" [406] studded tires if you need them. I found small wheels had issues on days when it was snowing hard and accumulating on the road. The cars would chew up this fresh snow into a gray mess that was very slippery because the snow crystals were rounded and didn't stick to another [studs wouldn't help on this]. Days like that I broke out my Surly Pugsley with 4" x 29er tires. If I didn't have such an exotic bike a 26" knobby MTB tire would have been my next option for riding during/just after big storms.
In terms of it being a good idea...if you want to ride that bike in the winter then go for it. I tended to do the same thing - limiting my winter riding to one or two bikes so I picked the ones I really wanted which were my Tikit and Pugsley.
Just respect the conditions and go slower/brake earlier than you normally would. I'm not a helmet guy for casual city riding in the summer, but in the winter I definitely would recommend a helmet and I even wore pads under my clothes on particularly slippery days.
Have fun with the Winter Mini!...