grumpyolddude

MSD and Peryn are on track. It's possible that your wiper arms are stripped and the drums are just spinning. If this iis the case, you'll probably just have to replace the wiper arms. If you remove the arms and can see the drums rotating, you've got your answer.
If it's damage to the transmission, which is under the cowl, parts and labor will be more expensive.

If you are hearing a humming, your motor is probably OK.

For future reference: clear all of the snow, ice or other debris from the windshield before you turn on the wipers. If they are stuck to the glass, or burdened with a heavy snow, you're likely to cause damage.

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"Regret can be a harder pill to swallow than failure .With failure you at least know you gave it a chance..." David Howard