If winterizing in the water need to use a plate clamped over the top of the sea strainer with a male air fitting. Attach air line, open seacock and blow air thru to empty water from seacock. Close the seacock and then remove air line from strainer.
To the OP question, if your on the hard I would leave them open. What ever small insect gets in there will be purged out in the spring. Now if the boat will be outside unused during the summer, I would close them so things like mud dobbers, or other winged insects don't build a nest