The straw/hay mulch you placed on top of the garlic after planting is beneficial and is sufficient for overwintering.  Creating a small "greenhouse" with a plastic sheet will likely cause more problems overwintering as it will allow for a wide range of temperature fluctuations throughout the winter months that have the potential of preventing dormancy or bring the garlic out of dormancy prematurely.  

Be sure to remove the mulch next spring and the garlic planting will benefit from fertilization in the spring.

More information about growing garlic can be found in the links below.  

https://www.extension.iastate.edu/news/2009/oct/061601.htm

https://store.extension.iastate.edu/product/Garlic (Click on the “Download” button it the middle of the page to download and open the free pdf file)

Further questions can be directed to your local county Extension office. This local resource can be very helpful since they are familiar with trends and issues in your part of the state. Click on this link to get the contact information for the Polk county Extension office. https://www.extension.iastate.edu/polk/

Happy gardening!

--Aaron

The link at the top of this page should take you to a form you can use to contact the Polk county office directly with your gardening question.  

https://www.extension.iastate.edu/polk/yard-gardenhorticulture

Here is the direct link to the form if that is easier for you: https://iastate.qualtrics.com/jfe/form/SV_cIbcoUvUcbGpGom

Happy gardening!

--Aaron