You can use tyvek* or some other kind of insulating foam board as a barrier in the ground.
Another easier option is mulch and lots of it!
I have an enclosure that is 10'x25',the soil temps stays around 40f all winter at around 4" and about the same at 8".
In a smaller enclosure 49"x44"the temps are around 37f.
In the smallest covers I use(33")the temps right now are 34ish.

My Basjoos are covered with 1 1/2 large trash cans of mulch and a plastic covering,we'll see how that works,
this winter should be a good test.
I am not really concerned about the Basjoos as I have heard they have survived to 0(F) or slightly less with little or no protection(?).

I would suggest if you are using smaller enclosures to pile AT LEAST 6" of mulch around the outside of your protection.
I protected some Washys last year in 10"cylinders but did not apply mulch outside them,dah-I think this is what got them as the plants themselves technically survived.
I think applying heavy mulch a good distance around your enclosures is the best bet,especially as your palms roots begin to reach out beyond their protection over time.

I was wondering about the same question about a month ago so I lifted up my palm protection and dug a little soil around the palm, and the soil wasnt frozen. It is possible that the soil is frozen farther down, but usually the soil doesnt freeze too deep here, but there is so much snow cover this year, that Im sure that it is pretty far down. My palms have lately been in the mid 50s in there protection during the day and the upper 30s at night. The sun is getting stronger now and the temperature is starting to reach the 60s in there on sunny days even when its cold. Im sure that with temperatures like that, the soil is unfrozen, and my protection isnt as strong a lot than others, its usually no more than 15F warmer in there than it is outside. Not sure about the surface soil temperature right now, but it is probably in the 40s and then a little farther down it might be in the mid 30s and then about 3 feet down, its probably back in the 40s (thats really just a very rough guess though)

My protection is only x-mas lights wrapped around the plant, a frost cloth, and then a plastic garbage bin (turned upside down) on top. I usually only keep the lights on during cold nights, but I want them to start seeing the upper 50s and 60s so they get ready for spring (but they haven't seen anything warmer than that because rapid growth in the winter is a really bad thing since the new growth is tender). Also almost all of my palms (especially my pindo palm) has seen no moisture since November because I didn't want the soil to be wet which would make rot a lot more likely.
As long as they are nice and dry, as well as above freezing as often as possible, they wont have problems. Mulch helps too espeically with larger palms. Jut put something (like a plastic tarp) over the mulch to keep it dry. I try to keep my palms from seeing below 20f because although they can handle much lower, I dont want too much damage.

Dont worry too much about the soil, if temps are constantly above freezing in your protection, the soil will thaw out underneath it. Good luck!

That makes much more sense. The point is to just get them through and not worry about any growth. Even my bananas inside grow very little and i water once a month. My Mexican Palms (seed grown) are still less then a foot tall (5 of them) and i have a bunch more seed i'll start this spring and then i'll have plenty of time to construct and plan a way to get them through...oh God...next winter! (trying to block that thought out of my head).... I'm just really sick of having so many plants in the house during winter and i can't afford to heat a greenhouse in this climate.

Heating coils. It keeps my coconut alive in the winter. I use the one with a built in thermostat. Plug it in and forget about it.

Here is a link that might be useful: Heating coils

I'm successful here in MN, which is among the coldest places I am aware of people wintering palms in ground.

Tips:
Enclosure wide enough for what it is covering.
Lots of leaf bags surrounding the outside of the enclosure.
Inside of enclosure kept above 35F, preferable in the mid 40s.

Rope light- like heating cable but uses way less power. Around the trunk of the tree(s) right at the dirt, then coveren by 6" cedar mulch to trap the heat down. Outer perimeter of the inside of the enclosure: mini Xmas lights or more rope lights, same placing under the mulch. On top of the heavy mulch, about a foot deep of dry leaves for extra insulation.

Last I checked, inside my enclosure for my large trachy the soil temp is in the upper 30s/low 40sF about 5 or 6 inches down.

Keep in mind that potted Washingtonias, trachys, and Chamaerops can be kept in a dark place kept just above freezing. My attached garage works well for this. On any plant, roots are more tender than foliage; solid freezing of palm roots is never a good thing. The danger is that you'll have a live top, but dead roots.

You can add the following palms (and cycads) to Steve's list of garage winterized species: Queen palms, Phoenix, Butia capitata, many Sabals except the most tender, Cycas revoluta, Dioon edule, and of course Rhaphidophyllum hysterix. Oh, and almost forgot--Livistona chinensis.

Depends on zone. Zones 7 or less needs ground and wind protection measures. Starting with foam, mulch and keep ground dry right before first big freeze by covering the palm and whole area.

Zone 8 still may need protection depending on palm and whether zone 8a or 8b.