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I use a zip cover in winter (been using my Little Shop of Hammocks Warrior in all 4 seasons now.)
I keep the part zipped near my feet so my top quilt stays in place and open up near my head to help venting and avoid condensation.
EDIT: Just to clarify, the "zip cover" on my hammock is a mesh bug net, not a solid top cover. Temperatures here in the winter can flirt with 0 degrees Fahrenheit but are generally in the teens to 30's in the winter on average I'd say. I don't feel the need for a solid top cover, but, then again, I do have a Hammock Gear full length underquilt rated to -10 degrees...
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Take this with a grain of salt as I have only been winter camping 3 times now but a top cover as mentioned here was just a condensation trap for me. I felt my tarp was enough and even that was starting to build up a bit of condesation during the night - I ended up opening up one of the doors just to vent everything out - but on the other 2 occasions I was fine without it - When I went without a tarp on the one occasion I had a bunch of frost on my sleeping bag in the night from my breath. HYOH, experiment, take advice, basically keep an open mind and "your system" will come to you. Have fun, enjoy the journey.