I have had a chive plant in the ground in Mandeville, LA for about 6 years and it has never frozen, even when it snowed. It is close to the house in an area that hold some water when it rains, but even in the drought that we just had this summer, it didn't droop from lack of rain. I have never covered it in the winter, here.
I love having it available all year round.

While simple logic may say that once you cut off the plug, the wire will be the same as one intended to be hard-wired, this is not a good idea. Doing this will negate any manufacturer's warranty on the equipment. Also, even worse, if that appliance should ever cause serious damage to your property, insurance may refuse to pay after discovering you DIY plug fix.

Give your local HVAC or Electrical contractor a call to have it done. Something that simple should only take about 30 min at market rate for your area.

Hope that helps