Is it possible for snow covering a car battery to drain the battery?

As in here

https://www.cambridge.org/core/journals/journal-of-glaciology/article/engineering-properties-of-snow/640B715A5752FE7DFD2C6EA2391AC00C

Reported values of d.c. conductivity for snow vary considerably, partly because there really is wide variation, and partly because there are measurement problems.

“cold” snow of unspecified density; in these studies, d.c. conductivity stayed within a surprisingly narrow range, from 9×10⁻⁷ to 4×10⁻⁶ Ω⁻¹ m⁻¹

and

conductivity increases by three orders of magnitude as temperature increases from —60 to — 10°C, and there is a sharper increase at temperatures above —10°C. The Tsuda, 1951 data (Fig. 28) show the rapid increase in conductivity that occurs as free-water content increases in “warm” snow.

To answer your question,

Is it possible that the snow covering the battery was the case of draining the battery?

It is possible but unlikely. The resistance of snow per meter, even when at close to 0 Celsius, is in the order of Mega ohms, unlikely to cause a more significant effect than the standby power consumption of automobile electronics and the self discharge of the battery. According to here https://shop.advanceautoparts.com/r/advice/car-technology/why-do-car-batteries-fail-in-winter

But as the chemical reaction occurs, the positive and negative lead plates are slowly coated with lead sulfate. This process is known as sulfation, and it reduces your battery's ability to hold a full charge.

freezing temperatures slow the chemical reactions occurring inside a lead acid battery, further reducing your battery's ability to perform.

It is more likely the temperature extremes exposed the problems on an already failing battery.

Water with impurities is a good conductor,  but snow is pure H2O, with a stable bond, and a poor conductor of electricity.  Factor in your positive terminal covered by a plastic cover with a plastic battery case.  So anything is possible, but not likely.

I live in a region with high winds and snow fall to hide cars in drafts or snowfall.  Getting snow under the hood is a common occurrence.  Never had a problem with dead batteries or starting car. 

Possible? Yes, assuming that the surface of the battery was not completely clean and some of the snow melted.