I would be more inclined to take a shovel on dayhikes --- on backpacking trips I'm carrying what I need to survive most situations, and I'm a bit less weight conscious on day trips.

But as OM says, it's in part about avalanche risk assessment as well making it easier to build shelters.

I tend to not carry a shovel as I tend to avoid avalanche zones for the most part when snowshoeing and XC/backcountry skiing. I hope to be doing some winter scrambles soon, however, which is the main reason I anticipate buying a (light, metal scoop) shovel.