Oberaar Glacier on the left and Unteraar Glacier on the right. Image From Google Earth.
Henri's father, Albert would surely have understood what he meant and as they were both friends of Louis Agassiz, and he probably had the Hôtel des Neuchâtelois in mind when Henri described the hut in question. The Hôtel des Neuchâtelois was a grand name for a stone and wood structure that Louis Agassiz used for shelter while studying the Aar galciers.
From Appleton's cyclopædia of American biography in reference to Agassiz
"During the summers frequent scientific excursions were made in the Jura and the Alps. These expeditions led to his (Agassiz) study of the glaciers, and in 1840 he published his first Études sur les glaciers, which gave there suits of his observations during the eight preceding summers. He had erected a station on the middle of the Aar glacier at a height of 8,000 feet above the sea and twelve miles from any human habitation, and from this now celebrated Hôtel des Neuchâtelois he conducted his experiments. In 1847 he published his Système glaciaire, in which he thoroughly discussed the chief phenomena of glaciers and more fully developed his views on their earlier extension."
An engraving of Agassiz's Hôtel de Neuchâtelois
The Lauteraar Hut which stands on the same site as the original Hôtel de Neuchâtelois
To read more about Henri's journey please find the adaptation of his entire voyage on Amazon.com.