One advantage of a long cane is that you can reach up and tap a branch so it will release its burden of snow before you walk under it. Well, it works sometimes. The world sounds different with a covering of snow. I navigate more by dead reckoning and less by my usual landmarks. Rain may not change the footing as much as snow and ice do, but it can change the sound of things in its own way.
Cars hissing by on wet streets mask other sounds.
Rustling raincoats do the same. Hats, scarves and hoods all influence what you hear in different ways, and you may want to think of that along with the weather. I am rarely out in rain so hard that it covers all other sounds. It may take longer to get places in the rain. I often listen harder and wait longer to know where things are and when things happen.