Dangling -y on made up adjectives

Of course you are totally free to make up needed words on the spot. This kind of ad-hoc language play is the innate right of all speakers.

The process follows certain rules, nevertheless. Let's take your example:

Friday nights are unwindy nights

At first read, without seeing your explanation, I thought this meant that Friday nights are characterized by a lack of wind. Here, "unwinding" would fit just right and obviate the need for a nonce coinage.

The usual thing is to flag or mark the novel use in some way, so I agree with your idea of "unwind-y," or potentially "unwind-ey" or something to alert the reader that unusual maneuvers are afoot. Unfortunately, "wind" (breeze) and "wind" (coiling) are homographs, so "unwindy" is unhappy.

Consider:

Friday nights are when I unwind. Friday nights are for unwinding. Friday nights I unwind.

While it's always acceptable to push the envelope, language-wise, you have to consider the puzzle you're presenting the reader and offer sufficient clues to allow smooth decoding.

Since unwindy is not an established word that a person would be familiar with, using the hyphen can assist the reader to parse the word properly.

The word unwindy has two possible parses:

• [[unwind]y] (adjectival form of "unwind")
• [un[windy]] (not windy, as in weather)

By writing the word as unwind-y, you help the reader to parse unwind as a unit, which can only be interpreted as the verb, and then apply the -y adjectivizing suffix.

Certainly, this construction is non-standard, but so is the word unwindy itself. If you want to use it in an informal context, go for it! Creating ad-hoc words is part of what makes language fun.