If you wouldn't keep your computer there, you shouldn't keep your kiln there. The problem with just covering it when you're not using it is that a storm could roll in while the kiln is still hot, and you wouldn't be able to cover it. Plus keeping it covered could also cause condensation and corrosion under the cover. I don't recommend kilns be put on wheels, as it's a sure way to damage the bricks, especially the floor. It may even be a code violation. Find a permanent indoor location for it.
Well, I don't have any actual scientific fact or study to back this up, but here's my educated guess based on what I know of kinesiology:
The "dominant" or "active" hand (right hand in a right-handed person, left hand in a lefty) is better suited for fine motor skills like writing, design carving, etc. The "passive" hand (the left hand in a righty; right hand in a lefty) is better suited for what is called "gross motor movements," using large muscle groups. Many times, the passive arm is actually a tiny bit stronger than the active arm. The body adapts to have a 'right tool for the right job' -- the passive hand does the brute force work so that your active hand doesn't get damaged (which would make it unable to do those fine motor skills).
Applied to pottery, as a right-handed person I am better able to center clay using my left hand - a gross motor movement, brute force. The counter-clockwise motion of the wheel brings the clay toward the heel of my left hand, making it easier for me to maneuver the clay without it catching on my hand. My right hand holds tools (fine motor movement) at an angle to the clay such that as the clay comes around (counter-clockwise), it again does not catch on the tool. If I were trying to do a scribbley design on a clockwise-moving wheel, I'd have to hold the tool at a very different angle to keep it from jabbing into the pot as the clay moves *toward* me instead of *away* from me on the right side.
A left-handed friend of mine who also does pottery has her wheel going clockwise for the same reasons, just reversed. Some lefties will throw "right-handed" (counter-clockwise wheel) in the same way that some southpaw athletes will do things right-handed.
I know very little about Asian pottery techniques; maybe they don't do the same things to their pots as Westerners do. Maybe they have a cultural tendency toward something closer to ambidextrousness (even if you aren't born ambidextrous, you can train yourself to do more with your passive hand -- I knew a gal in college who learned to write with both hands because the nuns always took the pencil out of her left hand and put it into her right!). Not that it's good or bad, just different.
I suppose that if your wheel is reversible, you can do what works best for you. And if it's not, you just have to adapt your techniques to work with what you have....