It's certainly possible to save money by turning appliances off, especially heating or cooling devices. It's true the water heater is typically the largest power consumer in a home after heat & a/c. Much depends, though, on the particular situation and personal factors. In this case it's things like external temperatures and the frequency & amounts of hot water use, the heater thermostat setting, and the efficiency of the heater tank (insulation). If you are trying to be frugal with hot water usage, you can probably save money vs somebody who is not so frugal, simply by not using much hot water. To know what the savings truly are, you would need to measure power consumption for a day in which no hot water is ever used, yet the tank remains fully heated. That's the base cost of keeping water heated. See how that compares to a day with the heater turned off 100% of the time. Then, compare your normal daily use vs the two baselines.
Having a timer on just 3 hours per day doesn't mean much for a thermostatically controlled heater. Obviously the heater is off when the timer is off, but the heater is mostly off any way, due to the thermostat. Most households use a substantial percentage of their water heater power in the mornings, when temperatures are cooler but the demand for hot water is high (showers & such).