It should be fine Cody! I have an orange and a grapefruit in my unheated greenhouse and they are both growing very well and both fruited last year If you feed it with a winter citrus feed that should help you with getting some fruit next year, good luck.
Don't forget to monitor the moisture levels through winter, too. Mine get a couple of drinks of tepid water throughout the winter.
i have grown a orange from a pip, its about 3" in height. What do i need to do, now that winter is on its way, to look after the plant.
Good Luck And Happy Gardening.
Keep it warm with plenty of light.