Although it's always safer to handwash your wools, as long as you are careful, there is no issue with washing wool-based fabrics in the washing machine. Just make sure to either wash your wools on the wool setting, or use a cold-water delicate wash. To ensure the best results, use a detergent that is designed for wool. 

You should also take care when drying your wools so as not to ruin the shape of the piece. Without wringing the garment, gently press the damp fabric back into shape on a towel, and then air dry it flat, rather than on a hanger. Do not put your wools into the dryer, as this will cause some serious shrinkage!