I can't imagine anyone not having a manual pump for such emergencies. Maybe they could melt a few buckets of snow, there might be some water there.
Anybody who has lived in the country knows that you fill clean containers with water BEFORE the any storm whether it be a blizzard or thunder storm.
Try a bucket shower, it works. You have 5 gallons giving you plenty of water to shower and shave. Remove the snow from your yard and melt it.
Man up.