Do you have a use in mind for this field...besides being just a field? Many cover crops might not winter-kill in your climate. Can you till it up a bit to get a cover crop established?

some of the farmers around me are planting radishes. Large, grow 2 or 3 feet down. They help with the drainage thru the clay and add a lot of organic matter. They also retain a good amount of nitrogen

Here is a link that might be useful: tillage radishes

I would like to grow Garlic in the field eventually. I want to be growing 1,000+ plants.

I'm not very familiar about the planting time for garlic. If you have standing water in wintertime, I suggest that you make some raised strips with walk and drainage channels between the raised strips through the field. The raised strips could be augmented with some organic matter. The dirt for raised strips simply comes from the channels.

Daikon radishes [tillage type] is my favorite cover crop and it winter kills here, but probably not out where you are, so you might have to mow and till it in spring.