Yes the sidewalk in front of your house is your responsibility. When I was a kid I made a ton of pennies shoveling that crap. Here’s a tip. Put up a sigh like you see at all parking lots. “WARNING! SNOW AND ICE MAY BE HAZARDOUS. (Well no kidding). Stick your snow shovel in the snow near the walk. Sign saying shovel it yourself. I can’t, and my wife WON’T. Then block the sidewalk with trash cans, lawn furniture or whatever.
Or you can buy my snowblower for a ton of dollars. I’m retired from that too. It’s a big one.