It's a little bit hard to tell you an exact date, but by reading the Quixote (1615) as it was originally written, and the letters of the spaniard conqueror Pedro de Valdivia to Charles V (1549), I could say that it wouldn't be that hard to talk to the people of, at least the XIV century: Yes, there are slighty changes in some words for example the transitions of some words from the F to the H and the modisms of that time, those would be the kind of headaches to get.

An older source, 'Las Siete Partidas' a spanish statuory code settled by Alfoso X sometime between 1256-65, but the version I've read was from 1491, it's understandable.

Now, the other old sources that I've read and that I remember in this moment is the 'Crónica Geral de Espanha de 1344' (written by the count of Barceló). I doubt if that would be a realiable source to answer you since it was written originally in portuguese and the text I've read was partially in spanish and partially in portuguese.

Sorry, for the disaster in the paragraphs, but I began looking for the pdfs I have while writting this. But again, for sure a modern spaniard (...actually, any spanish speaking person) would be able to understand and orally talk to anybody until at least the XIV century, another headache that one could have is the writting system: The Spanish began its standarization in 1713 with the foundation of the RAE (Royal Spaniard Academy), which would be continued sicne the late XIX century by the creation of local academies of the languague in many spanish speaking countries.