Basically you need the TV to be insulated from the elements, but having the enclosure air-tight like some have mentioned probably isnt the greatest idea... maybe some kind of plywood "locker" with a roof maybe?.
I think your single biggest concern is going to be keeping it dry, either from rain/condensation or whatever.. I've found the pix. tubes themselves tolerate temperature extremes pretty well, as long as the transition is gradual. You do have some temperature rated components in the set tho, as long as it isnt allowed to leave a range of say... 32F to 100F for any length of time you should be fine.
EDIT: I dont think the dog house would work. These TV's are designed to work in indoor conditions, that what you want to replicate in the enclosure. In a damp environment you'll have things start to rust in the set in a few weeks time. I really doubt how well your set will last under these conditions unless you can keep the humidity/water away. I've kept sets in an outdoor garage, and had the aquadag coating peel right off the tube... they just arent ment to be kept outdoors

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