You can go further back. The Old French ostel is from the Latin hospitale, meaning “inn” or “large house”, which is the noun form of the adjective hospitalis, from hospes, meaning “host”.

So the H in hotel is for host, kind of.

(you can go further back into the theoretical language Proto-Indo-European, but there’s no written record of it, so no letter H that we know of)

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Back during prohibition in the US, there was a product called Vine-Glo that was a brick of grape concentrate. It came with a warning: “After dissolving the brick in a gallon of water, do not place the liquid in a jug away in the cupboard for twenty days, because then it would turn into wine.”