Upon giving this some thought, I think the answer is going to depend on a LOT of factors. What kind of tub, is it well insulated, or not, 120 or 240V? Seperate circulation pump or not. How long of outage are we talking, days, weeks, ...? How cold, advice for North Dakota where they talk about getting up to 20 degrees for the daily high as a warm spell and lows of -20 being common, could be different than the Atlantic coast with lows in the low 20's.
For example where I live we rarely go more than 24-48 hours below freezing, but can occasionally get lows down around 10-15 degrees. Therefore exposed plumbing would be my main concern since it never stay's cold long enough for the bulk of the water to freeze. (the last time it was cold long enough for exposed water, ponds pools, etc. to freeze over here was 30 years ago, even then the ice was only a couple of inches thick). Therefore since my tub has a seperate circulation pump and I have a standby generator, making sure the circulation pump runs whenever the generator is running would be a priorty for me, but I would not need to worry about powering the heater which draws much more power.