Is it possible to format a hard-drive too often?

Formatting a drive is simply a matter of rearranging the bits, which is functionally no different from reading and writing files. I do agree with @soandos in that it is not a great way to maintain your OS, but it won't harm your drive, or reduce it's life significantly.

Hard drives are good for hundreds of thousands of write cycles, if not millions. Even the early generations of SSDs are good for a few thousand write cycles.

When quick-formatting your drive you are just rewriting the first few sectors once, and when reinstalling your OS you are writing a couple of gigabytes of data once, with a few sectors possibly being written to a few dozen times.

Multiply a few dozen writes by 4 times or so per year, and you are still nowhere near to causing any significant wear on the key sectors of the drive.

Memory paging (which is enabled by default in most installations) causes more wear to your drive in one day (by repeatedly writing to the same sectors) than you would in years of formatting with the frequency you described.

No.

Formatting your hard drive does not involve doing anything mechanically different compared to reading or writing to disk.

One way a drive could 'wear out' faster is if the operating system was doing a lot of memory caching to disk, also known as 'disk thrashing'. Another way is if your filesystem was heavily fragmented, and the disk had to traverse large sections of the hard drive platters to fetch data.

Formatting does not fall under any of the two above scenarios.

One additional thing a low level format does is add bad sectors to the bad sector list. As others have said this is killing a fly with a hand grenade. If you have enough bad sectors to slow down Windows, get a new drive.

Also, so many installs may make you sloppy when it comes to updating the OS or apps, making you more likely to get malware.

Technically, any use of a drive shortens the MTBF (Mean Time Before Failure, I think). But, as someone said, nowadays that's a huge number. Drives aren't guaranteed beyond that. But they will all eventually fail with use from simple wear and tear; they have moving parts and spin platters at incredible speeds and high temperature.

Low level formats aren't possible on new drives; bad sectors are mapped out by the firmware. Each cylinder of a disk has extra sector(s), and when a sector begins to fail, it is moved to the fresh sector and re-mapped. When the extra space on one cyl fills up (drive is really going bad) it borrows the next cyl's space. I'm not sure what that means to the defragment programs, but I assume they handle it properly or are completely blind to it.

I agree that formatting is no more damaging than any other function. Less than my StarCraft II game, by far!