HBO
The very first written description of Tyrion was from Jon Snow's point of view, in the early chapters of "A Game of Thrones":
Tyrion Lannister, the youngest of Lord Tywin's brook and by far the ugliest. All that the gods had given to Cersei and Jaime, they had denied Tyrion. He was a dwarf, half his brother's height, struggling to keep pace on stunted legs. His head was too large for his body, with a brute's squashed-in face beneath a swollen shelf of brow. One green eye and one black one peered out from under a lank of hair so blonde it seemed white.
So - ugly, mismatched eyes, with a brutish face and white-blonde hair. That doesn't sound much like Peter Dinklage.
Paul A. Hebert/Invision/AP
Here's one fan rendering of Tyrion's book description.
Henning Ludvigsen
If you're wondering why this Tyrion's nose is particularly gruesome, it's because the drawn scene takes place after the Battle of Blackwater (season 2 episode 9), where Tyrion was wounded. In the show, Tyrion is slashed across the face, leaving a scar up his cheek and on the bridge of his nose.
Helen Sloan/HBO/AP
Someone did the work of photoshopping Dinklage in order for fans to get an idea of what he would look like as a mangled Tyrion.
Here's another fan version of Tyrion, drawn by Cecilia Latella on DeviantArt. This one plays up the different colored eyes and blonde hair. She painted this in 2008 - before Dinklage was even cast for the role of Tyrion.
Cecilia Latella/DeviantArt
For more illustrations of how Tyrion might have looked, you can check out DeviantArt. In the meantime, we can be grateful to HBO for casting Peter Dinklage.