The same pump feeds pressure/ water into the hot water lines - the water just goes through the hot water heater between the pump and the faucet.
You should have a set of three valves next to the hot water heater to close off the heater input water, output water, and open up a bypass.
You never want to run antifreeze through the hot water heater. Find and turn the valves before you winterize.
You should also drain the hot water heater. Winterizing and later summerizing is a great time to replace the water heater anode and to flush out the hot water heater inside with a wand or small sprayer.