A lot of things will work electrically when wet, as long as the water film is thin relative to the size of the thing. For example, a wet dipole, no problem. A tiny coil where water droplets can short adjacent turns, not so much.
Water getting in coax, either the feedline, or as part of a balun or trap, is a problem. The water will wick down the shield, causing corrosion and dielectric loss. The coax is ruined. Best practice is to terminate the coax with connectors, then waterproof the connections with mastic or rubber tape.
Water facilitates corrosion. Galvanic corrosion between dissimilar metals happens faster with water. Sticking to one kind of metal (don't connect aluminium and copper), or using corrosion resistant metals (stainless steel), or protective coatings (paint) are often easier than avoiding all water.
Water is only part of the problem: in many climates snow and ice must also be considered. A coil may not be a problem in rain, but may be sufficient for sticky snow to accumulate in it. A thin film of water may not be significant, but packing a coil with wet snow could be a problem. Furthermore, freeze-thaw cycles can cause mechanical stress and eventual failure, especially in ferrite which is slightly porous. Accumulated snow and ice can increase the weight of antenna systems beyond the structure's capacity.
At microwave frequencies, the dielectric loss of water is more significant, and the dimensions of a water droplet approach something significant relative to wavelength.