brakes

Good brakes are important. The remedy you suggest is the way I would go. I would also flush out the old brake fluid while you are replacing the caliper (unless this has been already done within the last 2 years).
To prevent frozen calipers in the future, change pads when they are worn to approximately 50% of new thickness. As the pads wear, the caliper pistions pretrude more to compensate. This exposes the micropolished steel outer surface of the piston to the elements, and it corrodes. When you replace the pads and push/wind the piston back in, the corroded part jams in the cylinder bore. There is a piston seal that is supposed to prevent this, but it is really just a dust boot and does not block moisture unless you keep the lip well greased.