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Personally, I intend to leave mine on unless the weather is extremely warm. Low's of 20C or higher I may remove it.

Too chilly? Our friends South of the border were just out in a lot colder than -12C. :)
http://www.hammockforums.net/forum/showthread.php?p=918943#post918943

I haven't had any issues staying dry with the standard tarp. It's been used in some pretty heavy rain as well. I'm still making a larger one for giving more protection around the general hammock area...