I have a decent sized office with plenty of storage and this is what I keep in it:
If I got snowed in, I figure I could shut my office door and stay comfortable-ish for a while.
I also carry a 65L hiking pack in my vehicle (I know you said you don't drive but maybe you could have a look at the Ultralight hiking group? I'm sure you could get plenty of ideas for a fairly small lightweight bag). I have everything I need in my hiking pack to walk home. Tent/sleeping bag & pad/food/water filtration/Jetboil/etc. I hope I never have to but I could.
If you're worried about weight, you could always get some sort of cart like this.
Did a bit of searching. This looks like it might come close to what you're looking for.
https://www.amazon.ca/Trolley-Dolly-Shopping-Grocery-Foldable/dp/B00KXMB6TO