There are a few very real deterrents to moving your washer and dryer to your garage: First, I don't know what climate you live in, but yes - without additional heating, you risk water lines freezing in an unheated space. Since heating a garage quickly becomes expensive, even once it's insulated, you might find yourself spending far more money than you ever anticipated on clean clothes and convenience!
But there's something else in your question that concerns me: Your mention of dehumidifying your basement by removing the washer and dryer. This is an unwise motive. If your dryer is properly vented, it shouldn't be contributing to basement moisture.
If I were in your shoes, I'd concentrate on dehumidifying the basement by taking steps independent of the washer and dryer. And if you really need to make the washer and dryer more accessible, consider a stacked unit - a dryer on top of a washer - that is more likely to fit in your closet or your kitchen. There's a quality one from Santa Fe, and if that's too big, there are smaller appliances and models designed for apartments and compact homes. Good luck!