How to protect cacti in winter when it goes below 32F?

The cloche idea is good, but I think ideally it should be a light colored opaque color.  There may be a time when you need to keep them on through the day (or you forget to remove them), and you wouldn't want the sun to heat up the inside like a greenhouse.  Clay pots often work well, even with the hole on the top (because the pot would be up-side-down).  The hole would prevent condensation inside the cloche overnight, too.  The cloche is capturing ground heat rising from surface, which will be continuous, and preventing frost from forming on the cacti overnight by providing a "roof" above it.  If it only was insulating the warmer air inside it from outside temps, the captured heat wouldn't last very long.  I would use cloches very sparingly.  If the tags say hardy to 20F, I would certainly not cover them if temps were above that.

I don't think you'll need to protect cacti from cold winds.  A cactus (or any object) can't get any colder than the air temperature, no matter what the wind is like.  In addition, wind will keep the plants dry, which as you know, is important for cold hardiness.  

All this being said, please also consider that this "advice" is NOT coming from someone in your region, and is based on methods and concepts that work up here in Minnesota.  Hopefully someone with experience in your type of climate will improve upon my suggestions.

When your temps drop down to the teens do they stay that low for extended periods?

I agree with Rick. I have used clay pots over cold sensitive cacti. When they are dormant they do not need a lot of light. The pots keep the rain off and allow air flow. If the temps just dip down for a short period covering cactus can work, however there are no grantees over extended cold snaps.

I grow in a dry high desert environment that averages 10F but drops into the single digits for a week or two every winter. I have found that cold sensitive cacti benefits from being planted close to the south side of my house. The heat radiating through the ground and off the wall can give an additional 10 degrees.  I just don't grow semi hardies in the open garden any more. They seem to succumb to the cold eventually usually the first winter.

Every once in a while a semi hardy cactus, at one of the box stores, catches my eye and at less than three dollars a plant I feel like rolling the dice. It usually comes up snake eyes and  lose.

I found this website, where they sell plastic containers of any dimension

https://secure.ccwproducts.com/distributors.php

I was thinking of buying a container with a lid and I would cut the bottom of the container, stick in the ground over each plant, and have the lid available to open and close at my pleasure depending on whether there is going to be a cold spell or not. Plus I will be able to open and ventilate the plants for a few hours during the day just by unscrewing the lid!

And I also plan to tape white paper inside each container, so the sun would not burn the plant inside, and still they can receive enough light through the white paper!

I also made a sketch of what I have in my mid. What do you all think?

Better, but don't let the practicality and ease of you invention lure you into using them more often than absolutely necessary. 

Remember that even with tinted glass, you car can heat up quickly in the sun.  When the cactus is dormant, it wants to STAY dormant.  you don't want to confuse it with day time temps rising too high and signaling a return to growth.  Even with the lid tipped or cracked open, the temperature could rise to an unwanted level during the day.  Indeed, even with the lid completely off, the temp will be somewhat higher than the surrounding temperature.

I will use these protections only when I know that the temperature will approach 20F. I designed these cloches with the purpose of keeping the plants warmer than their minimum tolerable temperature, while keeping them dry as well. I know that both low temperatures and wet soil cause the cacti to die in the winter. These are not permanent structures, and they are easily removable. I also think that because warm air tends to move upward, I believe that even if I keep the lid open during the warmest days of January and February the plants would still go through the winter vernalization. I don't really believe that 3-5F warmer than the exterior weather would compromise the entire biological cycle of the cacti... But of course I am not a botanist and I just talk by common sense!!!

Manfroni wrote:

I don't really believe that 3-5F warmer than the exterior weather would compromise the entire biological cycle of the cacti... But of course I am not a botanist and I just talk by common sense!!!

You are certainly correct!  My point is that if even a simple vertical installation has an impact, how much more a cover, even cracked open.

I stand at the other end of the spectrum.  I will baby plants through the first year and only to the extent that literature claims is needed.  But after that, if they don't make it on their own than they are not for me!