I'm in North Texas and a 3 sided shelter works fine for my horses. Of the 6 farms I can think of in my immediate area with donkeys (some mini, some standard,) all run with cows and only one property has any sort of shelter besides trees. All donks are currently fluffy as can be, not a blanket in sight.
It's inexpensive to run a line or two of electric wire for extra security. I use a 5 mile solar charger for a single electric wire running around the perimeter of my 4.5 acre pasture, plus it powers two additional temporary fence sections of 3-rows of electric tape.
~Reserved Cash, 2011 AQHA gelding~
~Lark, 20-something Arabian mare~