we've NEVER winterized while plugged in and on 'city water', even at the Wakarusa service center in the dead of winter... they 'take' your coach into a heated building when it's being worked on. As long as you have your furnace or space heaters working inside your coach, you'll be fine. Don't use the city water hose during the overnight hours when it's more likely to freeze with no running water.
They are NICE people, and WANT you to be satisfied - give them ALL your needs - they'll help you, and may even do MORE than you even asked!
Been there several times... all good, very good.
two Campers, two Electric cars
former diesel pusher traveler