I've just put up a new shed with just sheathing. Where I live, which is SouthEast of Philadelphia, PA, the daytime high is now about 50 degrees (+ or -). In short, It's not warm enough out to put up shingles and have them properly seal up.
The question I have is this: If you're a gambling man (or woman) and you weren't putting the shingles on now (which I'm not until next Spring), would you bet that if you put tar paper up now, that even though I'm covering the roof with blue plastic for the Winter, the tar paper would still 'break down' over the Winter (crack, split, shrink, etc.) before next Spring? Another way to put this, would it be better to just cover the sheathing w/o tar papering with the blue plastic and do tar paper and shingling next Spring, or, go ahead and put the tar paper on now and cover it with blue plastic until Spring? My $$$ says to wait 'till next Spring to paper and shingle; don't install tar paper now (even though I'm covering the roof with blue plastic)