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.