Well, I've finally found an article about the missile defense decision in an Estonian newspaper. Eesti Päevaleht has an article today.
Urmas Paet, the Estonian Foreign Minister, has been visiting the US this week. He met with Hillary Clinton and others while he was in Washington. He also met earlier in the week with Anders Fogh Rasmussen, Secretary-General of NATO. Presumably all these meetings were part of the administration's getting out the word on the missile defense system.
In the Päevaleht article, Kadri Liik, the head of the think-tank that published a letter to Barack Obama signed by a number of eastern European intellectuals and former government officials said that she doesn't think that the decision is "a big tragedy," nor does she think (I'm being a bit loose here, but it's close) that the US is throwing them under the bus.
There's more in the Päevaleht article about NATO issues (there will be a NATO foreign ministers meeting in Tallinn next April) and energy issues than there is about the missile shield decision.