Gulltown is the port for the Vale. Catelyn and Roderick left from there to White Harbor and Petyr landed there when he wooed Lysa. Littlefinger stated to Mace that sailing to Gulltown in winter is dangerous, so I doubt a winter amphibious invasion is likely. Using the map on the inside of the covers of ASOIAF, Gulltown is on a penninsula... I'd say that even if a hostile force captured Gulltown moving up to the Vale would not be an easy proposition.
Entering the Vale at all is difficult. The road that Catelyn took ends at the Bloody Gate where legend states that a dozen invading armies dashed themselves to pieces in the Age of Heroes.
The Bloody Gate and the Eyrie comprise two nigh impregnable fortresses for the Arryns.
I've been to the Great Wall of China twice and I'd like to compare it to what I imagine the Bloody Gate to be like. The Great Wall is twenty-five to fifty feet in height and maybe fifteen to thirty feet in width. It has castles and guard posts every ten to twenty miles. It does not really sound like much at all, but it's strength is in it's location. The Great Wall runs along mountain ridges. Just to get to the Wall an army has to hike for days through the mountains.
I think the Bloody Gate would be similar. After climbing through mountains for days, an invading army would reach a defended wall. The army's supplies would be strung out and easy pickings. The army's approach would be known for days, if not weeks, in advance. Lugging siege equipment up there would be a logistical nightmare. Finally, assaulting the Gate from a forty-five degree or steeper slope would be exhausting.
The best way to defeat the Arryns would be to ally with the Mountain Clans and let them show a secret way around the Gate or mayhaps to bribe an Arryn general. In effect, this is what the invaders of China always did. They'd buy off a disgruntled general and just walk around or under the Wall.
I've been thinking on the accessibility of the Eyrie. There is only one way up, unless you can fly. It reminds me of Masada. I went to Masada in 1995. It is an ancient fortress built atop a mesa that is seperated from the rest of the Judean plateau. You've seen pictures of the Grand Canyon? Well, those sheer cliffs are similar to all sides of Masada. There is only one path to the top... it's single file and exposed to the defenders the entire way. The 900 Jewish defenders (at least half were women and children) held off the Roman Tenth Legion for two years. Since the Romans could not fly, the Jews could have lasted for decades. The Romans did the next best thing to flying, they built an enormous ramp from the nearest point of the Judean highlands over to Masada.
To get to the Eyrie, an army must take the fortress at it's base... the Gates of the Moon. After that, three castles straddle the narrow path up... Stone, Snow, and Sky. As long as the Eyrie has giant cisterns and arable land, there is no reason it could not hold out forever.
But holding the Eyrie against dragons might prove difficult at best. Dany should send in her dragons under cover of darkness. They would not need to kill the defenders in one attack. I imagine night after night after night of dragon raids would sap the defenders will quickly. If the dragons could kill everyone or drive most of the defenders down to Sky, then mayhaps the dragons could land a strike force on the summit. Being caught from below, above, and from the air would force the Arryns to surrender, I think.
Egg, what do you think about medieval siege operations in the mountains, medieval winter amphibious assaults, and dragon air superiority?