Is this a Jacuzzi Bathtub, or a full size Hot Tub? Unless it is a "Hot Tub" I wouldn't advertise it in the title.
I don't have Jacuzzi Bathtubs in any of my rentals, but I've installed them for myself in the last two places we've lived. The maximum water temperature coming out of the faucet can vary throughout the year depending upon the outside temperature and time of year. The "Hot" water is held at a fairly constant temperature, while the "Cold" water is going to reflect the temperature of the ground that the pipes feeding into your house is. Your Cold water is going to be colder in the winter, and warmer in the summer.
I don't know what your Water Heater is set to, but most hold the temperature somewhere between 110 and 120 degrees. The Size of your water heater and the temperature of the "Cold" water entering your house (and water heater) are going to determine how quickly you "Run out" of hot water. If you've got a 30 gallon water heater, and a 70 gallon bathtub, you're going to have warm water most of the time.
If the temperature was fine for you during the summer, it could be a simple matter of having the maximum temperature of the bathtub's mixing valve adjusted UP in the winter, so that the water temperature coming out of the spout is hotter. But if your water heater isn't big enough that alone isn't going to be much help.
Though not an exact ratio, think of it this way. If you take a gallon of water at 110 degrees, and add a gallon of 70 degree water to it, you're going to have two gallons of water at around 90 degrees. If instead of adding a gallon of 70 degree water, you add a gallon of 50 degree water, you're going to have two gallons of water somewhere around 80 degrees. I don't know how cold your water gets in Seattle in February.... but what if it's around 40 degrees? The max temperature is going to be around 75 degrees when you blend a 50/50 mix of Hot and Cold Water. If your water heater is storing 30 gallons, as you use the water in the tank it is replaced with Cold water.... So as soon as the Hot Water starts flowing, it begins to cool from the maximim temperature you have your water heater set to. When you've used half the water in that tank, the output temperature has fallen way below that maximum temperature.
You might get away with simply adjusting the maximum temperature in your water heater, and adjusting the mixing valve at the bathtub to increase the ratio of Hot vs. Cold water flowing into the tub (And you'll want to adjust it back down in the summer so you're not scalding your guests and wasting energy at the same time.)