'Settling' with weather usually means improving. It can mean that the wind is dropping. But in your case, since the sentence is referring to snow, it can mean that the rain/snow will reduce or stop. (edit) Another possible, and in fact on re-reading, the probable meaning is that the snow is settling on the ground, i.e. not melting and turning to slush.

Hi Talita, it has several meanings. Can you tell us more? Examples: you drop a bowl on the floor. It rolls around for a few seconds before it settles. Your house foundation is cracking. The house is settling. I purchased investments and they are settling tomorrow. I wanted a Cadillac but settled on a Chevy.

thanks

Settling is an extension of the word "Settle" which has multiple means. 1) To agree upon conditions e.g. We will settle the case in court. 2) To place in order e.g. to settle one's affairs 3) To migrate to another place, take up residence or colonize e.g. to settle in America 4) to Pay a bill e.g. to settle your account 5) To come to rest - This definition is the one used in your example. The snow soon comes to rest.