Looking at my numbers from last winter, just switching from summer tires to studded winter tires dropped my average speed about 17-20%. Some really slow days were significantly worse even than that. And if there were any way to account for muscle fatigue, it is probably even worse than those numbers - there is nothing quite as exhausting as fighting a nasty, cold headwind on studded tires.
For me, it is totally worth the extra work. I still love bicycle commuting *most* days through the winter. There is an intense satisfaction in beating a super-cold commute, sitting at the desk, and sipping the first hot cup of tea in the morning. I am definitely going to get after it again this winter.
The one thing that surprised me last winter is how nasty the combination of hard headwind and studded tires is. I am convinced that there is some kind of cumulative effect at work. If studded tires add X amount of work to riding, and a nasty cold headwind adds Y, the combination doesn't feel like X + Y, it "feels" like 1.5*(X + Y). Maybe it's just psychological. YMMV.
It's definitely worth it to keep riding through the winter, for many reasons (fitness, satisfaction, enjoyment, environment, all the same reasons you ride anyways). It's more challenging and more work, though. And one piece of advice... take the first couple of rides on studded tires EXTRA easy. Leave way early, and pedal easier than you think you should be. Go slow for a couple of full rides, until you get some miles on the new tires. They are different. If you charge hard right out of the gates on those things, you risk injury. I got a little hamstring tightness that way. I've read others who hurt themselves that way, too. Just plan on Slow, and if it goes better than that, it's a bonus.
It's really not as bad as this post probably reads. Get out there and enjoy some winter riding!