You can't do this without a 3rd party, unless your PC has a SIM card built in. And you simply aren't going to find a completely free party for this, since sending SMS messages costs money. I don't think anyone is willing to give away money like that. Perhaps you don't have to pay but you still end up "paying" by looking at a lot and a lot of ads, and probably also ads inside the SMS messages.
Most SMS services can be addressed via a "magic email address", which usually is something like "firstname.lastname@example.org". Just send a 1-line email of 140 characters or less to that address from the PC. Works great.
The hard part is making it general-purpose. Since the email address varies depending on the receiver's phone service provider, you have either know what that provider's email address conventions are or go through a generic gateway service that can find out and route it for you.
There's a fairly comprehensive list of the email address forms on the Wikipedia, including providers in both the US and in India.
Customer surveys are for companies who didn't pay proper attention to begin with.