Would it harm my stethoscope and spygmomanometer to leave them in my car all the time during the winter?

I don't think it will do the rubber tubing/bladder any favors. The metal / mechanical parts will be fine, of course, but ultimately, the tubing will probably suffer damage. I would bring them inside when you get home, leaving them in the same spot all the time, so you don't forget them. Also, I doubt your patients will appreciate a zero degree blood pressure cuff, or stethoscope against their arm.. The site below sites care of a 3M stethoscope, which states to avoid extreme heat, cold or heavy use of oils. All of these degrade the rubber tubing. I'm certain that the care of your blood pressure cuff and stethoscope would be similar whether it be 3M or not.

My Stethoscope