We just got a hot tub down here in the flatlands. As mentioned, the key is whether it’s hooked up to 110 or 220 volts. Our spa heats up 2 degrees per hour on 110 and 6 degrees per hour on 220. Because the pump has to run during heating, you save money with 220 because it heats up quicker.
So, depending on how often you come up to the mountains, you could keep the spa at a lower temp, during non-use, then turn it on when you arrive.
I imagine there is, or should be, some way to turn it on from the telephone or inter-web before you come up… 😉