I do carry some stuff in case I get stuck in the snow, as work out in the Oxfordshire countryside.
Includes a hat, gloves, sturdy boots, socks; airline-style blanket; Mora knife, multitool, folding shovel and folding saw; a Hexy stove, lighter and fuel; bottle of water, tea, tinned food; poncho, tent pegs and paracord.
I stick them in a 33ltr highlander pack, and just leave it in the boot of my car during the winter months. Came in very handy last year, when the road I took home froze over and everyone was stuck for four hours. After that little escapade, I added one of those self-lighting barbecue logs, and leave it in with the spare wheel.