yes that will be fine.  you are essentially just protecting the roots from wild temperature fluctuations.  the unprotected pot will warm and cool every day/night, and the temperature swings can be extreme.
you can wrap the pot in cloth/burlap and set it on the ground somewhere protected from wind and sun also.

Don,
   Thanks for the  reply. What do you mean by the sun also? I thought Pondies liked the sun. And the spot I keep my bonsai gets sun most of the day. It's the only place that doesn't get blasted by the high winds we have out here. Should it just be left in the shed its in now? It's a 10'x10' metal building with a small window so it gets a little indirect light and is not insulated so it gets cold at night, but the temp fluctuations aren't as great. I'm just not comfortable with it getting that little light. However I'm new to pines and don't know very much about them.

Once frozen, it won't need any sun.  You can keep it in 100% shade or even in a cold building with no light.

That wasn't my point though.  What I meant is this: keep sun off the pot.  Sun shining on a pot will warm it up, especially an unprotected dark colored pot.  Dark colors absorb light and heat up.  A constant freezing/ thawing cycle can damage the roots.  

There is another thread in this forum, I believe discussing greenhouses, in which Bill Valavanis provides information on cold storage of his collection.  Check it out.  You will find good information there.
 

Don, he is in Zone 8b-9a. The low temps are not that low, like you and I think of. The tree won't be frozen- it will get some twenties, maybe on an exceptionally cold night in the teens, the days will be 40's-50's plus most of the time. The wind is probably the killer in desert.

Don, he is in Zone 8b-9a. The low temps are not that low, like you and I think of. The tree won't be frozen- it will get some twenties, maybe on an exceptionally cold night in the teens, the days will be 40's-50's plus most of the time. The wind is probably the killer in desert.

well then, just set it on the ground in a spot protected from the wind.  you don't need to do anything more.

I just placed mine on the ground and mulched up to the rim of the wooden box.  I didn't bury it, is that ok?

yes, that's fine, though covering the pot/soil surface helps.  its just extra insulation.  ponderosa are tolerant of extreme low temps with little protection.

Don, he is in Zone 8b-9a. The low temps are not that low, like you and I think of. The tree won't be frozen- it will get some twenties, maybe on an exceptionally cold night in the teens, the days will be 40's-50's plus most of the time. The wind is probably the killer in desert.

That's what I was thinking as well.  I live in zone 7, and I generally leave my ponderosas out on my benches for most of the winter (in a spot where they generally have a decent amount of wind protection).  On very cold days, I'll sometimes bring them into my detached unheated garage with my other trees, but otherwise, they seem to be quite fine outside for the winter.  

I'd put them on the ground, but I'm worried about rabbits, chipmunks and other varmints nibbling them.  I have a few trees in the ground that I'm growing out, and the damn critters love to chew off the bark and low hanging branches.  

If you do leave your ponderosas outside, I've found that the needles take on more of a grayish hue which could be disconcerting if you're not expecting that.  They end up greening up quite nicely once spring rolls around.

When I put them on the ground, I have them in an area that I put a welded mesh wire around the perimeter.  Well spent $40/50ft.

I've been thinking about doing that too - that's well worth the money.