For medium and small scale outdoor shows, fabric or plastic (fastfold type) screens may be practical depending on the size of the screen you need.. You can also use several white bed sheets sewn together and suspended by ropes between scaffolds as a screen. To cut down wind resistance, make several small "V" shaped cuts in the screen for the air to pass through.
If you have plenty of laser power, a very effective screen can be made from white mosquitoes type netting or mesh sewn together.  This forms a scrim where the laser beams are visible from the projector to the screen and beyond. With smoke in the air, this gives the illusion of images floating in space.  More laser power is needed as there is less material to interrupt the beam and form the image on the projection surface.  The up side is that this type of screen has almost no wind resistance.  

Example of a mesh screen - Photo courtesy of New Wave Lasers

The photo above shows an example of a large mesh screen which has been suspended across the front of a stage from scaffolding towers on either side.  Not shown are the wires from the top of the scaffolds to the ground to brace the structures.  Note the vertical seams in the screen.  This is almost unavoidable as this type of mesh fabric is not available in a very wide format.  The seams do not generally present a problem or distract from the audience's enjoyment of the show.

In large outdoor venues, you may have to use the side of a building or other less-than-ideal surface as the laser projection screen. If it is not possible to have a light coloured projection surface, you may have to use a more powerful laser to overcome the light loss from a non-light coloured screen. If you have a long throw, you can keep the line widths in the image small by using a large frame laser or a beam expansion telescope to up-coliminate the beam.
Most times there is just no way around having to provide the projection surface yourself. The simplest and most cost-effective way to do this is to use standard construction scaffolding weighed down with concrete blocks or bricks. Thin plywood attached to timber supports and painted white forms the projection surface. 

12 X 16 Foot scaffolding and plywood screen diagram

The diagram above shows an outdoor screen built with three sections of scaffolding towers. The bottoms of the towers are weighed down with concrete construction blocks set onto wood planks. This design can be scaled up or down as needed, provided that additional bricks or concrete blocks are used to weigh down the scaffolding towers (to prevent the wind from blowing the structure over). If you are expecting windy conditions, you can use 4' X 4' thin plywood panels and leave 1/4" gaps between them. This will allow some air to travel through the screen relieving the air pressure.