Well rain they basically just get a soaked moodlet, and you have to be outside for some time before you get cold enough to freeze and the gigs aren't that long.
If the weather is really bad you can perform for tips inside, nothing says you have to do it outside, I had a sim performing inside a library recently, they may not make a lot of money depending who's about but you still get the job experience. Or buy a portable fire pit so they can warm themselves up if needed while out and about. You could also use it or a fireplace to warm yourself before a gig, the warmed moodlet lasts 3 hours if I recall correctly, long enough to perform a show.
So far the only sim i've had actually freeze was sleeping outside in a sleeping bag for some hours, other than that they just get the feeling chilly moodlet.
