You don't HAVE to change your water that soon, it's not a bad idea, but not mandatory. I live in the Minneapolis area, and wouldn't change the water in my spa in January unless some repair issue forced me to.
I usually change our spa water as late in the year as I can get away with, usually between early November and Thanksgiving if the weather holds. Then I coast on that water until it warms up in March.
You can do partial water changes in the winter if you need to- Bill (our esteemed moderator) does this, I think, and he could possibly give you the details if you're interested.