I would definitely carry a shovel if I had a car. Weather is unpredictable, so is the terrain you have to cross. One time I had to go home with a teacher after my father was unable to pick me up due to heavy snow fall (normally used to cycle home as well!).

In the 1970s British infantry used to carry a full size shovel with them! Strapped to their 58' pattern rucksack/poncho holder. That says something. In Desert Storm the UKSF carried just the shovel and improvised a stick with what they could find once in their operational area...

PS Lofty Wiseman Urban Survival Manual also recommends carrying one