Thats weird, this happens to me, its like a pulsing vibration outside that makes the walls vibrate a little but is loud. It lasts usually about 20 minutes in total but the pulses last a few seconds.
I dont know what it can be (I live in south florida btw so I cant give you an opinion on the snow thing)

How close is the sound to the breaker panel?
Heat pump for heat?

Killed the power to any circuits in that area and removed the outlets and switch covers to check for back stabbed wiring, burn marks, loose wiring?

We are having the same issue! It started last night at 1am. we have an old home with many ungrounded outlets. I admit one outlet is overused and it is on that wall, right next to our bed that this vibration continues to occur. It kept us up all night. At shakes the windows and wall and sounds very mechanical. It lasts for maybe one second or two and seems to happen in a cluster and will go on for 10 or 15 minutes. Then it seems to quiet down but it comes back, soft at first then back to the heavy vibration.

There are no water pipes in this wall that I know of. It is by a street and hospital but is not being caused by cars or trucks driving by, I am sure of that. I have no appliances in the attic above or the living room below. It is not a living creature, definitely a mechanical type of pattern.

When I first heard the noise I searched through the house and while looking my furnace clicked on and my fridge clicked on. I mention that because the noise was happening while both of those appliances were off, and neither of them are creating the vibrations.

It is very cold and we just had a blast of snow and more to come. I have a wife and one-year old and am worried about a fire. We are having a new electrical panel put in within the next week or two, weather-depending, along with new grounding but this vibration just started happening and we already have the work scheduled.

I can only believe it is electrical at this point because there are only wires in the wall where the vibrations are occurring. Someone suggested turning off the power at the main switch and seeing if the noise stops. We will do that tonight to confirm if it is electrical. I read somewhere it can be an electrical arc within the walls, so I am praying our house does not burn down. I have unplugged EVERYTHING from the outlet on the wall which has vibrations, but that did not stop the problem.

Anyone who has a solid solution to this or knows what we should do, please help. THANK YOU FOR HELPING!

If we do get it resolved, I will post our resolution for those of you having the a similar problem.

Did you ever find out what was wrong?? I am having the same problem. I think. Its a loud buzzing sound that has been coming from my wall. It only lasts a few seconds but this is the second day that is has woken me up from my sleep! At first I thought it was my tv or maybe the power strip that I have my tv plugged into. I honestly have no clue. I tried googling it (which brought me here :P) and yours in the only one that sounds similar to my problem.

Somewhere in my walls or ceiling, there is a loud buzzing sound that lasts only one or two seconds. I thought it was a loud, raspy doorbell, but my doorbell sounds very pleasant. It happens rarely--twice last year, once yesterday, and once just now.

I am very familiar with electrical sounds. This is too loud and too rare to be a transformer hum. Possibly relevant: It has been raining heavily here in Florida. I wonder if it is some sort of mositure warning buzzer installed in the 1980s.