Re: car emergency supplies, we learned to carry a vehicle survival kit when we lived in Canada, and we weren't even living in a rural area. It's advised for winter travel especially, because cars going off road in snow or ice is a common hazard, but I find it handy to have all items in place year round.
The basics:
Matches, in a waterproof container
Several candles in metal cans – they are a heat source as well as providing light. Keep a flashlight in your car as well.
Water bottles
A metal cup - for heating water over a candle, melting ice or snow, or emergency purifying of outdoor water sources.
A blanket or two. Fleece is great.
My additions:
High-energy non-perishable snacks - granola bars, nuts, dried fruit, jerky. For years we stored our stash in an old child's lunchbox. A few packets of tea, instant coffee, or instant soup.
A 3-day supply of all vital medications.
A pocket mini-tool such as Swiss Army knife or leatherman, if you don't carry one regularly. I have one on my keychain.
1 warm hat, stretch gloves, and pair of dry socks for each family member.
Paper and pencil.
Hand sanitizer or towelettes.
Something to use as a shovel or scoop, to keep airflow to the vehicle if you are caught in heavy snow or your vehicle has overturned.
A small square of red cloth to mount on car antenna or a branch as a distress flag.
Better to stay with the vehicle if it's safe to inhabit.
If you do choose to leave the vehicle, leave a note for searchers. Blazing a trail with obviously broken or knifemarked branches or leaving other markings is vital for directing both yourself and searchers.
Other tips upthread are duly noted.
Knock on wood, we haven't needed to use this stuff in 25+ years. But if we ever have a stranding incident, we'll be somewhat prepared.