I was wondering if plants could absorb fine ice dust mixed into the soil. That is, without a thick layer of snow on the ground, but with traces of ice in the soil.
As an extension of this, I wonder about a plant's ability to make use of such grains of ice, melting them into water and using them.
I suppose that raises the question of how the plant will generate enough heat to melt the ice, since clearly its environment is failing to melt the ice for it. Chemical thermal process, perhaps?
Common table salt melts at 801 degrees Celcius, yet a glass of water will do it at room temperature. So you are quite right when you say that there is likely some other way to "melt" the ice into a form that the plant can use. However, melting ice is an endothermic reaction (takes energy), and that energy has to come from somewhere - thus either the plant must expend energy, or the environment will grow colder and reduce the effectiveness of whatever is melting the ice.
You also have the issue that solid chunks of ice - even very small ones - are not readily transported around within a plant, nor absorbed by the root system.
Hence, I propose:
These plants are relatively rare, and do not like growing near each other (as the cooling of the ground caused by other similar plants hinders their antifreeze), and prefer areas where the ground is maintained at a constant temperature by some external source (eg near inhabited buildings, near flowing rivers or the sea - both of which are excellent heat(cold) sinks for the ground temperature).
One limitation of this system is that ice-chunks in the soil are not easily replaced. Once the ice near to the roots is gone, so is the source of water for the plant. This means either:
In the comments, Madlozoz notes that antifreeze protiens can't melt ice. This is because they work by inhibiting crystallization when ice starts to form. Instead he proposes alcohol, which may well make the plant be favoured by local wildlife.... Other than that, some types of sugars may work. At any rate, there are some plausable sounding options for antifreeze. Take your pick.
I will work form the assumption that your plant is not frozen solid; that is, it is alive and functioning well. A plant cannot be frozen since it depends on liquid transport in the xylem and phloem to move around the minerals and nutrients it needs to live.
If you plant is already operating at a temperature above freezing, and the surrounding ground is slightly below freezing, it is reasonable for the plant to simply add enough heat to the environment to melt the surrounding ground. There are plants that generate significant amounts of excess heat. Many plants spend lots of energy on 'showy' features not strictly needed for survival, such as fruits or flowers. Your plants could use this excess energy to heat the ground to recover ice dust as liquid water, which the plant then absorbs. The good news is that soil is a good insulator; the heat the plant generates would not have to be too much to keep its roots at, say 5 Celsius.
The process of heat generation, called thermogenesis, is a byproduct of cellular respiration. This is actually the same process that warm-blooded mammals use to generate heat to regulate their body temperatures. There exist plants such as the skunk cabbage, voodoo lily, and dwarf mistletoe that use the same process to generate heat for various reasons.
So, your plant can simply be 'exothermic' in the sense that it regulates the temperature in its root system to be high enough above freezing that it can recover water from ice dust in the surrounding soil.
You need to invent some new biochemistry. Earth bound plants essentially stop when soil temps are below about 5 C. Roots have enough stuff dissolved in the water that they don't freeze until -1 or -2 C, and some species load up on alcohols and sugars and can freeze into glasses. Lodgepole pine survives -70C.
But they don't metabolize at those temps. There would be merit in checking this fact with plants in the arctic tundra. My recollection is that they don't do anything until the surface of the ground reaches about 6C. But the biologists keep finding extremophiles.
As an example of this: Treeline can be well defined: 60 days a year with a high greater than 10C. Below that the trees can't generate enough energy to cope with wear and tear.
You could plausible have a plant that anchored to ice by dissolving the ice with salts along with generating heat.
Along with that, you could have shallow roots that worked when they were thawed, and stopped when frozen.
