I'm wondering what the process of courting and becoming married would've been like in Feudal Japan. I'm specifically asking about the nobility here, but I would be interested to know if the process and tradition differed, and by how much, compared to the peasant class. Additionally, how much freedom would the man or woman have had in the selection of their spouse? Was it predominately arranged by the families?
I think it would be helpful if you could clarify what you mean with "feudal" Japan:
I would understand the Edo-period - the 17th century onward - as "feudal" (if I'd be forced to use the term at all), which excludes the entire medieval period. However, various forms of warrior rule had already been emerging in the 12th century (of which the most enduring model was the "shogunate" one), and the term "feudal" is often misappropriated to refer to the entire period of "warrior government."
Next, in relation to this, the term nobility is not clear, since if you speak of feudal Japan, you probably mean warriors. But the words nobility or aristocracy would typically be interpreted as the court aristocracy.
Both of these aspects are rather important, since they have a huge impact on the scope of an answer:
Customs and traditions were different within court, warrior, and commoner society. Morever, customs did change over time. For example, the rights and roles of warrior women in the 12-13th century were very different from those of samurai wives in the 17-19th, which naturally also reflected on the institution of marriage!
To give just one example, there used to be empresses (i.e., spouses to the emperor) with a privileged status until the later 14th century (I forgot the exact date), when the institution was abolished and the emperor no longer had a specific wife (or several) with privileged standing anymore; after that, he only had amorous relationships with his attendants. So, changes in customs can be quite significant!
Since a total overview would be frankly a huge endeavor, it might be helpful if you could specify this a bit!