Fat bikes and tires offer more traction, and that means a more stable and secure ride. When snow starts getting on the tires, for a normal bike, it can become troublesome. Same is true for mud. For basic commutes, I don't think you would have to worry about battery power. You should easily be able to keep it charged between rides. The drive power will depend on your needs—if you like a lot of assist or not. Also note some bikes do not have a throttle. They are pedal assist only.
I ride a 2.3 CTS Rockhawk in the back and a 2.2 Maxxis Crossmark in the front for my winter bike. It's a GT Tempest, and this combination does incredibly well outside of very deep snow. So, it's definitely feasible to get a normal ebike, but you'll want to be running a 2.3 tire in the back like I do for good traction.
I bet you’d be good with with a normal e bike, I live in Denver and a colleague at work rides a mountain bike to work in the winter with no studded tires or anything and says it’s no problem even in the snow. But I’d imagine if you just got a set of studded tires that you put on in the winter and switched them out with normal tires in the summer, so you could also have a fun e bike to ride the rest of the year, you’d be perfect.
FAT BIKES are by far the best e-bikes you can get.
The tires are thick and wide which means you can ride on sand, grass and marsh. Small potholes aren't a problem either.
I think you should take a look at Rad bikes. Specifically the Rad Rover 6. Take a look at Aventon Pace 350 too.
These bikes are best for commuting and you won't have any problems on campus with comfort and quickness. Another reason I'm recommending these is the step-through frame. This makes it easy and quick to mount the bike and is perfect for quick stops. You'll find e-bikes prices to more or less be the same under similar specs and warranty. So make your choice based on the fit and aesthetics after you've chosen the specs
A fat e-bike is a good option, but it didn't work for me as I use a bike most of the time in my daily life and it's too heavy for me. But for trips in winter or over rough terrain, this is a good option. They are also very stable, another huge plus.