What is the most economical way to store a small aircraft in a place with severe weather?
Location matters.  Where are you located?  A hangar is not as important in a dry climate like Las Vegas as it is in, say, Miami.

It may make sense to pay more for a hangar.  Leaving a plane exposed to the elements you describe (0° - 100°, snow, wind, sun) will do damage over time.  The plane won't corrode into a heap but little things will start to require extra attention.  Those little things will add up at annual time.  It's unavoidable.  Having the hangar is another layer of protection that, in my opinion, is well worth the cost.  If a hangar is simply unworkable then think about a covered tie down. A covered tie down plus a decent cabin cover can accomplish about 75% of what a hangar offers at half the price.  You won't have complete protection from hail, vermin, or thieves but that's not a deal breaker.  Just lock the doors and keep the insurance up to date.

Are you considering a simple plane like a 150 (all metal, "affordable"), a tube and fabric plane, or something with more complexity like a Bonanza or Mooney?  Maybe a C-150 with rough paint, a worn interior, and old avionics that aren't worth stealing will do just fine outside.  If you buy something with good paint and interior (or fabric covering) you'll want to protect it.  New P&amp;I costs thousands and thousands of dollars so it's much cheaper to keep a pretty plane pretty than to make an ugly plane pretty.  The costs to re-cover a plane in fabric can cost tens of thousands depending on the amount of fabric and complexity of the paint scheme.  Other airplane-specific considerations like corrosion on Mooney's steel structure (see Mooney Service Bulletin 208) or a Bonanza's magnesium control surfaces should be factors in your decision as well.  Finally, when you go to sell the plane a buyer will likely feel much better about a plane that was hangared than one that was parked outside.

One piece of (unsolicited) advice: draw up a conservative budget assuming that costs will be higher than expected.  Budget for a hangar, $1M smooth insurance, and a tough annual during the first year of ownership.  Multiply this number by 1.5 at the very least.  This is a "bad case" first-year cost (don't worry, it gets better as you settle into ownership).  If you can absorb that cost without feeling any pain then you're ready for ownership.  If you can't...who cares?  Buy the plane anyway!

We can give you a more complete answer if you know the answers to the following questions:


where are you based?
what kinds of planes are you looking at?
what is the current condition of this hypothetical plane?
what's your maximum annual ownership budget?