I couldn't fit all this into tweets so i've made a short post here with some pics to help illustrate what i'm trying to say.
I've looked at the the names of the castles and villages in the Vale to see if there might be a clue to a possible 'back door' to the top of the mountain. With no textual evidence and some wild speculation all wrapped in the shiniest foil coating, there could be one.
Wickenden (circled)
Wickenden is the seat of House Waxley in the Vale of Arryn. The town is located on the northern shore of the Bay of Crabs, northwest of Crackclaw Point. It is famous for making scented beeswax candles. A Wiki of Ice and Fire Wickenden
House Waxley of Wickenden is a noble house from Wickenden in the south of the Vale. They are sworn to House Arryn of the Eyrie. The names Wickenden and Waxley come from the wicks and wax used in the bees wax candles produced in the village. The coat of arms of House Waxley are six white candles with red flames and their words are- 'Light in the darkness'
 | |
| Coat of arms | Six candles, white with red flames, within silver candle holders, on a grey field within a black border (Cendrée, six candles white in holders argent inflamed gules, within a bordure sable) |
|---|---|
| Words | Light in Darkness |
| Seat | Wickenden |
| Lord | Ser Edmund Waxley |
| Region | Vale of Arryn |
| Title | The Knight of Wickenden |
| Overlord | House Arryn |
Wickenden- Wick-end-den
Wick etymology- Verb
wick (third-person singular simple present wicks, present participle wicking, simple past and past participle wicked)
(transitive) To convey or draw off (liquid) by capillary action.-
The fabric wicks perspiration away from the body.
(intransitive, of a liquid) To traverse (i.e. be conveyed by capillary action) through a wick or other porous material, as water through a sponge. Usually followed by through.-
The moisture slowly wicked through the wood.
Traveling through this 'back door' would be 'wicking' through the mountains to the top of the Giant's Lance.
My own theory about there once being a weirwood at the top of the mountain would make the snow covered mountain look like a white candle burning with a red flame, like the candles in the arms of House Waxley
