*Please read this answer entirely, it’s actually important*
Whether or not you can use lasers outdoors is actually two separate questions. The first question is whether or not the lasers themselves are rated for outdoor use, and the second question is whether or not it is legal to use lasers outside. The answer to both is “sometimes”.
First, we can weatherize almost any model we make, but off the shelf they are a bit more sensitive than your average laptop. Unless you have a weatherized laser system, it is best to treat your laser as you would your computer. If you would feel comfortable using your laptop outside for short periods of time, your laser should be fine as well. However, just as you would not leave your laptop outside all day or night, nor should you leave your laser. Protecting it from excessive humidity, rain and extreme temperatures is essential.
The second part of this answer is for U.S. laserists. If you are outside of the U.S. please check your local laws.
The short answer is that if you want to do an outdoor show in the United States, check with your local FAA field office to see what they recommend. Be honest with them about what you want to do and they will point you in the right direction.
In the U.S., there are two kinds of outdoor shows: terminated (where all of the beams stop on a tent, or the side of a barn, etc.) and unterminated (where the beams either by design or even by accident might shoot up into the sky). The real issue with unterminated beam shows is that they might hit airplanes which is a SERIOUS NO-NO. Technically, the FAA should be able to approve or disapprove all outdoor laser shows. Recently, though, some field offices have expressed a lack of desire to review terminated laser shows, because the beams will never enter navigable airspace. However, one of the single most deceptive characteristics of laser is that when it is shot up into the night sky, it LOOKS like it stops a couple hundred feet up. This is not at all true – a single low powered laser can shoot for MILES, so caution is very advisable.