William Ray said:
I am saying that a blanket of snow eliminates most radiative heat loss from the soil, and slows (assuming an air temperature below 0C) conductive heat loss. As a result, the soil under the snow will often be warmer than it would be without the snow. What effect that has on crocuses I cannot say.
Fundamentally, the layer of snow on the ground is no different than a layer of fiberglass insulation on the ground, with the exception of the fact that the snow melts at a lower temperature than the fiberglass. So long as the temperatures involved are such that the "insulating stuff", whatever it is, doesn't melt, it functions as an insulator and decreases thermal flux across it. Given that the Earth beneath the snow provides a practically infinite reservoir of heat energy, during periods when that thermal flux would generally be "out of the soil", putting an insulator in the way results in the soil being warmer than in the absence of the insulator.
When water melts at 0C, the water formed is also at 0C. This would happen at the ground surface. The water formed would seep into the pores of the snow above. As long as there is any snow left at the ground surface, the water and snow would have to be at thermal equilibrium at 0 C. So, with snow on the ground, the temperature at the ground surface could never get higher than 0 C. I stand by this, and
@jbriggs444 seems to agree with me.
Here is a heat balance at the surface of the ground that captures the mechanisms you discussed above. Let q(t) be the upward heat flux from the ground surface and let ##\lambda## be the heat of melting (334 J/gm) of snow. The heat balance is:
$$-\rho \lambda \frac{d\delta}{dt}=q(t)-k\frac{(0-T_{air})}{\delta}$$where k is the thermal conductivity of the snow layer (typically, 0.045W/m.C for dry snow), ##\rho## is the bulk density of the snow (typically 100 kg/m^3 for dry snow). The second term on the right hand side represents the rate at which heat is conducted away from the interface through the snow layer to the surrounding air above. The overall right hand side represents the net upward flux of heat into the interface. It is equal to the rate at which ice melts to form water at the surface times the heat of melting (the left hand side). The melting causes the snow layer to decrease in thickness (from below), as captured by the minus sign on the left hand side..
Even if the heat conduction through the snow layer were zero (k = 0), the above equation would reduce to $$-\rho \lambda \frac{d\delta}{dt}=q(t)$$ Under these circumstances, the temperature at the surface would remain at 0 C while the snow is melting (from below), and the melting rate would be given by: $$\frac{d\delta}{dt}=-\frac{q}{\rho \lambda}$$ Back to the original equation, if the air temperature above the layer were below 0C, the melting rate would slow down.
Melting would stop all together if the air temperature were low enough. The air temperature for this to happen would be
$$T_{air}=-\frac{q\delta}{k}$$ If the air temperature dropped below this value, the temperature at the surface would actually drop below 0C, and would be given by
$$T_{surface}=T_{air}+\frac{q\delta}{k}<0$$
