Like a bikeshed made from pole and sheet?
I noticed an improvised shelter’s description which shows that it is capable of protecting fire from rain but I did not test it yet
I’ve never been brave enough to light a fire on an improvised shelter. I always assumed it would just burn the shelter down.
EDIT: As for the original question, the only constructions are the wood oven and the fireplace. Both of those protect from rain.
Don’t think so, but a lean-to would be a great level 0/1 construction item that you can put a fire pit next to, to help reduce wind and rain exposure outdoors using a couple heavy sticks and pine boughs.
Fire pits are easy to build (just rocks), but they’re actually kind of a PITA in CDDA due to the large number of rocks you need, requiring you to scour acres of land and juggle early game inventory limits.
Post-apocalyptic New England may pose many environmental survival challenges in real life, but a shortage of rocks is not one of them! There are few places around here where you couldn’t collect a fire pit’s worth of rocks within 50ft of wherever you start at random in about 1 minute, frankly, they shouldn’t require you to have anything in your inventory at all its so trivial. 
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