How can I send SMS from my PC using my Android Phone (Galaxy S3)

Use Airdroid. It gives SMS and much more. And it is web based so you don't need to install a client on your machine.

MyPhoneExplorer the best software i know!! Works really great, its fast and needs no installation. It works via USB, WLAN or bluetooth.

you don't need any extra apps or software as Samsung has this already covered. Samsung kies air is capable of doing all this & more using WiFi. It only works for Samsung devices tho. :))