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.