We recently purchased a 120V hot tub. We installed it in our indoor pool area, which was unheated this winter as the insulation is not completed. The unit is insulated with what appears to be low-density spray foam and has a ~2" insulated cover. The bottom of the tub (below the footwell) doesn't seem to have any insulation.
I recorded the power use in January using a P4400 when the air temperature averaged 32F/0C and the temperature set to 103F/39C. The tub was using 14kWh/day which works out to $50/mth @11.8c/kWh. When we switched to TOD rates I put a timer on it so it only comes on during off-peak rates, cutting electrical costs down to around $20/mth. It will drop from 103F at 7am when the power shuts off to the low 90's by the evening so we turn on the power manually in advance when we plan to use it during the week.
A tub 8' * 3' high has a surface area of 126sf, so with a 100F delta-T and R10 insulation the heat loss would be 1260BTU/hr or 370W. Therefore a well-insulated outdoor tub should cost around $30/mth to operate in Jan/Feb at standard power rates or half that for off-peak.