I don't think you need to mow or do much under the feeder other than sickle down the real tall weeds. They will find them pretty quick and take care of anything in their way.

I put corn in mine during the Fall &Winter only. I used to do it all year, but it wasn't getting to the deer (mostly birds and small critters). I am not convinced that my deer use it much at all unless there is almost nothing for them. I check the feeder in the winter & find very few tracks. I've thought about switching to something that only or mostly would be consumed by Deer, but cost has always been an issue. I would be interested to hear what others are doing.