What should I consider when storing a light aircraft outdoors for several months?
Are you in a wet or coastal environment?  You can store a "Cessna type" plane outside for a few months and be ok.  Most flight school planes live outside for years and do just fine.

Don't use a tarp.  You might damage antennas, windows, or paint.  Custom fitted covers are good but they're also expensive.

Don't just start the plane and let it idle.  That hurts the engine more than it helps.  To do any good, the engine must reach and sustain normal operating temperature until the moisture boils off.  A quick flight can accomplish this.