Packing tape seems very adhesive and possibly too thin. Some riders use "helicopter tape". I think its a 3M product and at most airports you will find mechanics using it.

I use it on the frames of my bikes where the cable rubs against the frame. And on the frame where the frame pump may bump against the frame.

But since I'm in Southern Calif, I don't see any salt, snow, ice roads anymore. I was from Roseville, MI so I know what you mean.