Largely transparent. If you have a lot of wood around the antenna, rather than air it might detune it to a small degree. Higher moisture content will have greater impact.
Not really worried about it IMHO.
Thinking about EMC testing for regulatory purposes you can have structures around the equipment under test to protect them from weather, but they must not perturb the measurements. The typical structure is made of wood and uses dowel pins to hold everything together, to avoid using nails or screws. Likewise the table the EUT is sitting on is wooden.