Oh, not a storage solution but a wonderful way to get by the first hour and have virtually nothing to lug around the rest of the day. This trick is time honored and still used by professional bike racers. Newspaper. Use a Single full sheet folded at it natural fold. Tuck the rectangle inside your jersey, over the rest of your layers and pull up so the corners start around your shoulders. Rip the center down 6" and fold back like a shirt with an open top button.

This is nearly as warm as a vest, keeps your back doing good cooling work and pulls out easily while riding. Not hard to fold and stuff into a jersey pocket while riding and if the weather changes later, can be a real blessing. (I've put that newspaper back in when rain started many times, A real help in hanging on to body heat when wet and tired.)

If you watch the pro bike racing and can find footage of the rest of the peloton cresting a high summit on a cool day, you will see riders sitting up and stuffing newspaper, just like riders did 100 years ago because 1) it works really well and 2) those riders are the lesser riders who are back in the large bunch or by themselves. They don't have a team car handing them a sponsored jacket. Their job is to finish the stage in good shape and health so they can get up tomorrow and do this work again. Means getting down the mountain and staying warm using their own resources.. A lot like what many of us have to do every ride.

If you can, select higher quality newspaper. Less print wearing off onto your jersey.

Ben