Vinegar would not harm the water pump. All many of the winterizing kits do is put in valves so you can connect the suction side of the pump to an external hose rather than the water tank, so doing that manually is equivalent. You will, of course, need to disconnect the water tank or remove that hose or it won't be able to suction out of your container.
I would actually suggest putting in valves etc. so that you can do this without removing and replacing hoses, and you'd then have the winterizing setup ready. If you have a fill valve for the city water connection (as opposed to only a gravity fill port), you can also use the pump to fill the water tank from a container with the winterizing setup by opening that fill valve and setting the others to pump from the external source.