Well, you could try taking the caps lock off.

Other than that there isn't a ton you can do. Depending on the style of the muffler you may be able to make an exhaust diverter and direct the exhaust downward.

btw, why can't you run it at 6am? When there it is snowing, people generally understand you gotta clear it out. I've never had anyone compain to me for running the snow blower at 5am even. Now the vacuum cleaner, that's another story.

Yup, people in snow country accept that snow removal is going to take place at whatever time necessary........and to those who don`t , don`t worry about them.

You don`t want to add any additional muffling to your engine, it will choke it down on power. Joecool`s idea of a deflector sounds like a good idea as long as it`s not restrictive. You can buy muffler deflectors at good OPE shops that screw or rivet onto your muffler. Just be sure to pull the muffler and get any metal shavings out before running the engine if you do any drilling on it.

Most of the people on my street have their drivway cleared buy Profesionals. They have great big tractors that remove the snow from a standard drivway in one sweep. They are "oblidged" to clear the snow BEFORE 6 (or something) so the people can drive out and go to work. The noise and flashing yellow lights will wake anything up...Nobody complains, it has to be done.
As for making it quieter, wear ear plugs.

Anything you do to the exhaust that doesn't cause a resstriction is going to be so big and bulky it probably wouldn't be practical. Keep in mind there is a substantial volume of noise coming from the carb and snowblowers generally have no air filter to knock down most of it. You might try using a big block of foam that you can stuff into the air box around the carb opening to reduce noise from that source. Filters are not used on snow blowers because they aren't needed and a filter can ice over causing an over rich fuel condition. Any block of foam you stuff in and around the carb needs to be easily and quickly removed in case this happens while running and for removal to allow to dry out when not using.

If you decide to go the route of the air filter, you will need to re-tune the carb or it will be running real rich afterwards.

'Well, you could try taking the caps lock off'
That is funny.

Here is an idea:
First study the current muffler and how it is mounted to the cylinder. After your familiar with the engine, run a search for Radio Controlled boat engine silencers. Many of the larger RC toys use string trimmer, blower or chainsaw engines. Finding a silencer for the exhaust port size shouldnt be that difficult. Another crude method that may work is to take a large Chili Bean can and fit standard flameproof fiberglass insulation into it. You would then mount the bean can over your snow blower engine's muffler. Just make sure there is enough air flow through the can so you dont choke the engine's air flow. You could wire mount the can untill you come up with a permanent solution, or even take it on and off depending upon the time that you want to use it. For sure a tip of the hat to you for being a nice neighbor!