"Probably all, or nearly all, who have experienced a cold winter, are familiar with the cheery cry of the snow as it is pressed against a hard surface by the steel tire of a wagon, for instance, or even onto a pavement by the heels of one's boots."
Those words were written many decades ago by the physicist W.J. Humphreys in a book called Physics of the Air. Humphreys went on to suggest that creaking of snow is connected with very cold temperatures.
Freezing Temperatures Lead To Loud Snow
Humphreys said that when the temperature is just below freezing and snow is easily packed into snowballs, footsteps and rolling wheels won't create much sound.
His reasoning is based on the fact that applying pressure to ice lowers its melting temperature. If ice is so warm that it's about to melt anyway say, at a temperature of 30 or 31 degrees Fahrenheit then a little pressure will be all that is necessary to melt it.
Snowflakes And Ice Crystals
Snowflakes are small ice crystals. Snowflakes near their melting temperature can, through hand pressure, be made to fuse into a snowball by a process of melting and re-freezing. The snow yields to pressure "gently and progressively" and doesn't make sound.
On the other hand, if the snow is very cold, far below its melting temperature, even the pressure of a boot heel or a wagon wheel won't melt it.
The snow is powdery and won't form snowballs.
Instead, pressure just makes the ice crystals crush and slip over each other as dry particles. That "abrupt and jerky" motion of the dry ice crystals causes vibration and sound, according to Humphreys' book.
So W.J. Humphreys claimed that snow creaks when the weather is very cold, but not when the weather is only moderately cold. Does that claim jibe with your experience?