If you want to carry a shovel that doesn’t take up a lot of space is one of those army surplus entrenching tools, or “E-tool”. They’re not very expensive too.
CC
I have the e-tool, Fiskars axe, bastard file, Swedish Saw, etc. Those are pack in my GOOD bag.
I carry the collapsible snow shovel for moving large amounts of materials.
I also carry collapsible snow shoes and ice cleats whenever I head into snow country.
After snowboarding for a day, I frequently have to walk quite distance across icy conditions, from my hotel to the casinos, where I end up eating and drinking.
I find it makes walking much safer and wayyyyyy easier to traverse ice covered roads and sidewalks, with little fear of gravity reminding me “Hey! Would have made walking in my tennis shoes so much easier”.
Here is the ice cleat I typically use:
http://ecx.images-amazon.com/images/I/51Ye8c3bVCL._SY300_.jpg