. . .I work in a facility in which we will probably be expected to stay put for the duration of an emergency, and not go home. How do you all prepare your work kit? . . .
Sounds like essential services, government or utilities. . . whatever.
Good advice from the guys above. (I read in flat mode so everybody's "above".) I agree with the other suggestions. You need to nail down how much your employer will provide and go from there. First thing will probably be a change of clothes, underwear, socks and maybe outerwear consistent with blizzard conditions -- duffel bag. If you drive to work, part of your car kit could be part of your office kit. That duffel bag is part of my truck kit -- my stranded in the mountains kit. I also have MRE's, water, sleeping bag, pad, tent and blankets as part of the kit. My walking kit (BOB) is also in the back of the truck to supplement.
If you really think they'll expect you to stay at work for extended periods, then they must be going to make arrangements for food. Does your employer have a cafeteria that will stay open during a blizzard/power outage; otherwise, how do you think they'll feed you? How much food do they stock? Pizza Hut and Dominoes probably won't be open.
Once you get a handle on your employer's contribution you'll have a much better idea of how much you need to backfill. If it appears that they haven't given it much thought, you might also volunteer to assist in that management role. Take on the job and tell them what they need and make arrangements for employees to be able to store supplies on-site -- storage lockers would be a good start.
As for me, my employer will provide my office and that's it. I can't store stuff there since there are way too many others through the spaces, nothing would be secure. Hence, my truck kit doubles as my office kit. I could be very comfortable camping out on carpet.
I remember when I was at the Pentagon they made a determination of essential vs non-essential personnel to cut back on support requirements to what was needed for essential folks. My boss made the decision that no one in our office was essential; when situations arose, we all went home and turned off the lights. Determining who in your office is essential during an emergency would be a good thing. Do all the secretaries really need to stay for the duration? Less $$over-time stress on the company budget and support requirements may be reduced. $.02