As a matter of fact, there is no sound / are no sounds while it's snowing, but I prefer that silence , [like] time goes slowly.

"like" by itself does't sound quite right to me. Here are a few alternatives:
but I prefer that silence; it's as if time slows down.
but I prefer that silence, when time seems to slow down.
but I prefer that silence with the slow passing of time.

Maybe I like nature and quitet peaceful times.

I think it's more natural to say "times" since you are referring to different experiences / times, including by the sea and when it snows.