That is a toughie, AX. I use an auto air conditioner metal stem dial thermometer, available for $5 at any auto parts store. Perfect for soil temps...but...the numbers are too small for photography.
I also have a wireless thermometer on the porch, which reads out by radio signal to a little LCD screen on my desk. But it takes batteries and I am not sure the moisture, the batteries, and the radio signal under the soil would work satisfactory.
I have another one that sticks to my window with an LCD readout...numbers big enough...but probably not suitable to bury.
Good question, is your soil not frozen, under the snow? Will the temp rise due to the insulating effect of the snow--assuming the deeper soil is warmer?
Very windy here, but only about an inch of snow fell.
I have about 4 tiny sprouts from perennial rye seed I planted in a cup plunged into the soil on November 17th. Air temp is 33 tonight.