Promises translates as promise, and the meaning here can come from "notice"
As the saying goes, "a heavy snow indicates a good harvest"
this means
As the saying goes, "a heavy snow is a promise of a good harvest."
As the saying goes, "a heavy snow is a sign of a bumper harvest."
I hope it will be helpful to you, and I also hope to click "Choose a satisfactory answer" to adopt it in time. Thank you.