Obtain a
styrofoam box from a pharmacy (their drugs come to them in such
boxes) and line it with thermal blankets, obtained from a thrift
store.
Cut an oval
hole (big enough for a cat to get through) in the box, the bottom
of the hole being about 6 inches from the bottom of the box so
that snow, rain and slush don't get into the box.
Tape the
box top onto the box with duct tape, making several rounds of
the box to make sure the taping is secure.
Put the
box in a protected area such as your back porch, with the open
hole facing the wall of the house so that the box is sheltered
from snow and harsh winds.
Put something
heavy enough (a couple of bricks) on top of the box so that it
won't be blown away in a blizzard. Careful, you don't want the
styrofoam box to cave in with the weight of the bricks and the
snow. Another option, if you can: build another stronger wooden
shelter around it and put heavy items on top of the wooden shelter.
After every
snowfall, make sure to clear away the hole's entrance and a path
for the cat. Do this in a delicate manner so as not to panic the
cat, speaking softly and continually to the cat as you work.
Your doing
this might well save an animal's life. At the same time, the cat
may well learn that you're a helper, and this might make it easier
for you to get the cat to go into a carrying case around March,
so you can get the cat neutered before the spring mating season.