Yorkies have only a single coat, but cutting the hair does nothing but make it shorter. It will grow back. So, cut it...grow it out...cut it again in a different style...your choice, or whatever makes your Yorkie comfortable. With shorter hair, your Yorkie may need warmer clothes in winter, but even with longer coats, my Yorkies appreciate their clothes when it's chilly weather. There are cute Yorkie hairstyles you can check out at:
Yorkie Hair Styles
Several here have had 'not so great' grooming experiences, so to be as 'safe' as possible, be sure to make your wishes known, and take a photo with you, to the groomer...and be very specific with any instructions.
