I've found an old blog referring to old medieval windows made of horn with an example of an extant window in the "barley hall" in york. A few old forums said the horn was soaked for 3 months cut and flattened into sheets for windows. Some of the examples are fairly transparent even as seen on a horn window on a copy of "St. Cyprian's Works [M.9.19]". But no official resources or references actually saying how they made them.
On one of the forums a user also mentioned on the topic a cloth treated in some way to allow light in, but couldn't remember what country it was in. It was suggested it might have been an oil, so I tried to find a translucent oilcloth and got nothing but modern products, so I tried oilcloth windows and eventually found a tweet of all things with a picture example from in "Poplar cottage" tagging the Weald & Downland Living Museum. The official website doesn't mention oilcloth, oil cloth, or oil cloth windows, once. I went through 32 pages trying to find out more about their windows and none of them say much about them other than them being open. I'd love to learn more about these.
I've found a wiki page for "greased paper windows" used in the 1800s by American pioneers. It doesn't go into much detail
I've heard of but found no resources for oiled skin being used. No photo examples, no books, forums or blogs popping up that actually say anything about them.
And the one thing I found a resource for is the first greenhouse called the Specularium made for Roman emperor Tiberius. It used thinly cut mica for the windows.
If you have any other examples of transparent or translucent windows I'd love to hear about them!
I too have often heard about greased paper being used for early 18th c. colonial American windows, but I can't provide a good source for it, alas, let alone one for the medieval period.
There was considerable use of horn as a material pre-19th c. in many of the applications where we'd use plastic now: buttons, frames for glasses, cups, spoons, and combs. Horn scraped thin was certainly used to make windows for lanterns, so it does not seem impossible it could have been used to make windows for houses, also. But horn does not weather very well- sun, heat, rain and insects would certainly have an effect. So, I would not assume it happened.
The tradesman was called "horner" in English, but is listed here in Diderot's Encyclopedia as "travail avec la corne".
Because of the use of finely scrimshawed powder horns in the colonial US, there's a number of people who have revived the trade, and have a website: https://www.hornguild.org/ Though they are mostly 18th c. re-enactors, I think they would find your window question quite interesting. Horn is thermoplastic and softens in boiling water, but mostly the people who work it now heat it in oil to get it very hot (fryers for chips/french fries are apparently very useful). Once it's pulled from the oil, the horn is trimmed, cut, and pressed to flatten it. As some horns are more translucent than others, some selection is important.
If you can read French, there's also an interesting paper posted online on the use of horn in late medieval Avignon. It does not mention it being used in windows for houses. Chazottes, Marie-Astrid (2019)L'exploitation de la corne à Avignon à la fin du Moyen Âge
In Iceland, they could be made of a calf’s caul, stretched thin on hoops. There are examples in the turf house museum of Laufás (north Iceland), which dates back to at least the 16th century. Some if the ones there are modern recreations, although I could find no information about them beyond this picture on the museum’s website. I saw them there only this summer!
I found a 19th century source in English, which you can read it here, for free (page 216).
Edit: I found another source, a text in Icelandic. It's called Womens Work in the 11th Century (page 270). Basically, there is very little information until the 18th century, and the sources that do mention them omit the material they were made from: it is nevertheless clear that glass was a luxury and very rarely used. However, what is mentioned (and pictured on the page) is the calf-caul window, and a description of their manufacture. The caul was washed and scraped, then inflated to dry out, at which point it could be stored. The frame was made of a light/flexible wood like willow. They were not always round, and if square many were assembled like panes of glass in a window. The caul was wetted before it was stretched out on the frame. Interestingly, the sources quoted states that they would allow in as much light as 'the clearest glass' although they were prone to rupture in bad weather. This type of window could also be made out of a foal's caul, which were stronger but let in less light.
Another option was fish skin, from a skate, if cauls were not available or considered to expensive (!), also scraped and stretched. This was was regarded as women's work, and was likely the responsibility of the women looking after the cows during calving. The text states that these techniques were likely to have been brought over from Norway during settlement.