Unless you live in an extremely, excessively polluted urban environment, natural rain should be fine, provided that it's not a heavy storm. My Jax really enjoys a light summer rain, especially those odd ones that happen while the sun is shining. I took him out several times last year.
In addition to his mister which goes off several times a day, about every other morning, I try give him a long shower with my handheld pressure sprayer. I use hot water from the tap so the spray is lukewarm. Some days, he could care less but other days, he really enjoys the warm shower.