I seem to be the only crotchety old man here not seduced by the current fatbike trend, so feel free to keep that in mind while reading on.
Fatbikes were invented only a year or two ago (or at least that's when the copycatting exploded: the Norco fatbike in that video didn't exist before 2014). So that means tons of people have been successfully bike commuting in winter long before fatbikes existed, even in Toronto. A fatbike might make it easier, but easier enough to justify the $1500+ cost? (and depending on the fluffy snow/dry pavement ratio, that's debatable, since the fatbike will make you a lot slower on dry pavement than a normal bike.)
I bought a set of studded tires for my normal commuter bike some years back. They're definitely great on ice, but the drag, sluggishness, and noise on dry pavement tend to put me off, so I've really gotten very little use out of them, much less than I expected at the time. But maybe my route, plus the snow-clearing efforts in Chicagoland, lead to far fewer snow/ice-covered days and miles than you'd encounter, so it's easier for me to just not bike on those days, and use my normal tires for all the other winter days?
I would just say that you actually work out the math on how bad the winters have to be over how many years in order for your bus fares to come close to the price of the bike. Seems like $1500 could pay for a lot of bus rides. And do those studs come out in the summer? Or do you need to spend another $120 to get a second set of stud-free fat-tires? Or would the fatbike be used exclusively as a snowy-weather commuter?
Bike commuting through a snowy winter usually trashes bike components to hell (due to salt + water), so people often use a crappy old bike for their winter commuter rather than a brand-new really-expensive bike. So the idea of spending on a "high quality" bike and expecting it to last for many winters may be the wrong approach. It seems like you could put those studs just as easily into tires on an old mountain bike you pick up on Craiglist, and that would be a more versatile and useful bike anyway.
Hmm, but your mention of needing to get a backpack really throws me off. Are you not already commuting to work by bike? If not, I'd say don't get any bike for winter commuting until you're a lot more familiar with summer commuting. Spend the summer doing that, and as many days this winter as you can, and then for next winter you'll have a lot more knowledge to help you decide what might be beneficial (if anything) to help you ride those days you couldn't this winter.