Being that this is probably my favorite TV show, should I now go read the books? Or would that ruin the enjoyment and surprise of the series?
WhenSpoiler:Stark got beheaded... I was blown away.. epic moment in TV to kill off the most likeable and best character.
I would hate to ruin moments like that for myself.
I might suggest reading the books only as far as the show has gone. It might help fill in some background details and expand some plot points without giving too much away. If you like the books a lot, keep reading; if you want to keep the show unspoiled, then just wait for a bit.
If you really like the show, though, I'd be very tempted to say that you should not read book 3 until after season 3. And avoid any discussions of the books during that period. A Storm of Swords is very, very intense.