Winnebago says to close them in our owner's manual and mentions the possibility of bugs (spiders, etc) getting in but that applies only to the freshwater drain valve under the coach if it doesn't have a screen on the outlet.
Some say that leaving valves open can result in seals drying out and future drips, etc.
I blow out the lines with an air compressor @ <40 psi. Don't forget to: drain the water heater and enable the bypass valve, add RV antifreeze to the shower and sink drains, run air through the toilet valve (or antifreeze through whole system). In my case, draining all freshwater lines and applying air pressure is sufficient. The only antifreeze I use is for the shower, sink drains, a little in the black water tank through the toilet, and a very small amount through a pickup tube at the water pump so that the filter and innards don't freeze. If I don't do the water pump here, I remove the sediment bowl at the pump and empty it. I like this limited antifreeze approach because it avoids tasting remnants of RV antifreeze for the first several outings next spring. I've also found that the thickness of the RV antifreeze can clog the bathroom sink screen in my case.
Winnebago speaks of both the air compressor and antifreeze method in the owner's manual and closing all valves after the procedure.
History: '08 View, '05 Chinook, '01 Jamboree 24D, '78 Apache Popup, 81 Komfort Tlr,
84 Mazda B2000 'w canopy,
Tent from wedding shower in '96