I was an every day Minnesota winter commuter with a 5 mile commute for a number of years. I'm now just a regular winter rider. I've ridden a lot in the 0 F. to -20 F. temp. On thing that taught me--there's a lot of difference between 0 F. and -20 F -- just as much or more than there is between 0 F and 20 F. Which means I don't know what -40 F. is like. The only cold-based mechanical issue I've had with three bike (oil bath Raleigh Sports 3 Spd IGH, early derailleur mountain bike and a 5 Spd SA IGH bike with mechanical disk brakes) was slow to no-existent shifting on the modern 5 Spd IGH. This basically made the 5 Spd into a one speed in below 0 F. cold. I got the hub filled with better low temp grease last fall and it then shifted all last winter (lowest temp: single digits below zero F.)

Snow can be an issue. I don't know about fat bikes with 4 inch tires in deep rutted snow (only taken trial rides on them). But on conventional width tires, you learn as best you can to ride the ruts, spin through loose undisturbed snow (more work, but kinda fun), and yes, portage your bike over snow banks or drifts. Rim brakes can have issues with snow to slush turns to ice build-up. So far I've not seen that on my disks.

On rides like yours, if you dress right, you'll be warmer than getting into a car and waiting for it to warm up. Use lighter than you'd think wind proof layer, and then insulation layers under that as needed. You will probably need full face covering at the lower range of temps including goggles. Goggle fogging is an issue I've yet to solve. On my shorter rides that means ridding with goggles, have the antifog treatment work to clear them a couple of times until that washes out and then finishing the ride's last part with no goggles before frostbite can set in. Mittens or handlebar poggies are required at the lower range of your temps. If you use mittens, make sure your controls work with mittens. If you already ski or do other winter exercise you already know this clothing stuff.

Yes, you want studs. No reason to go without them in winter biking where ice may be present in my opinion.

Yes, batteries work differently at those temps. I had good luck with regular Duracell like batteries in lights kept inside and warm until needed.

Yes, you aren't going to fix a flat tire or broken chain at these temps. You're going to walk your bike home or use another option.

I don't know enough about your winter climate, but here in MN, I'm proud that we can figure out how to ride at -20 F. -- but frankly it's more fun and less trouble to ride at 0 F to 20 above zero , which is really the more typical winter ride here. Similarly, riding is fresh light snow is fun, riding in frozen ruts days later less so.