It appears the decision to cast Peter Dinklage was made for two main reasons.
First (and arguably foremost), he's very hot property in Hollywood. A quick look at his Wikipedia page can show the amount of awards and nominations he's been up for since Game of Thrones debuted. He also regularly tops fan polls regarding their favorite character. All of this adds up to a convincing reason to cast him in a film (similar to someone like Bryan Cranston, from Breaking Bad, starring in Godzilla).
Secondly, his short stature does appear to be significant - as it has left many observers questioning the decision and making links between his disorder (anchondroplasia) and his character's dislike of mutants.
Peter Dinklage was certainly aware of this. In an interview which also involved Bryan Singer (the director) the following dialogue took place:
To hear "X-Men: Days of Future Past" director Bryan Singer tell it,
however, Trask has a lot in common with no less than Adolf Hitler.
Singer: “Trask is, ultimately, a peace lover. He feels that humanity will go
on fighting each other unless they find some common element to unite
against,” the filmmaker told "Empire" magazine. “Perhaps as Hitler
used the Jews as a scapegoat to bond the darker parts of Europe, he’s
doing the same thing with mutants. There’s also something interesting
about his size. I’m sure he went very underestimated throughout his
life. Trask comments on that — I don’t know if it’ll be in the final
picture — but he says, ‘I was underestimated, so do not underestimate
Peter Dinklage, who plays Trask, said he “wouldn’t go so far as
[comparing Trask with] Hitler,” but acknowledged similarities between
Dinklage: “I am this guy who’s four and a half feet tall, but my life doesn’t
constantly address it,” the "Game of Thrones" star explained. “With me
playing that role, I had to think about that stuff. I’m not going to
play my violin, but with my dwarfism, I’m a bit of a mutant. I can’t
move metal or anything, but I thought of it as self-loathing.”
“Deep down, Trask can be quite sensitive about that aspect of
himself,” he continued. “And sorry to go back to Hitler, but he wasn’t
a six foot, perfect blond Aryan. He was a short, funny looking fellow.
And talk about a mustache!”
So you can see, both actor and director have made no attempt to hide Dinklage's and thus Trask's stature (which is only an issue in the movie, as in the comics he is of an average height). Instead, they've used it to explain some of the prejudices he may feel, given the prejudices he's been exposed to his whole life.
Ultimately, I'd say Dinklage was simply cast as he's such a popular commodity in Hollywood at the moment. But his short stature certainly adds an interesting dimension to the character of Trask and provides extra motivations for his actions.