Currently on common HTML forms, all the fields are cleared when you refresh the page or navigate away and back to it. Would it be good or bad UX to store values in cookies as you type and restore them again on page load? Obviously not passwords.
I think fundamentally yes.
Firefox have started doing this as part of their basic functionality (citation needed), however, as site owner you can be cleverer, remembering things like marked map points, or bespoke, site specific field selections.
The problem is that when a a form is served it can only be populated with data that the server knows about, coming from a session or database. This is a snapshot from the past.
This leaves the client in a similar situation to anyone editing anything on a computer when something interupts them, like a powercut, and work can be lost. All effort should be made to save this work, in any context.
This sort of functionality is very similar to automatic save, which is implemented by our very own SE in a web context, but has been a stalwart of well built desktop software for years. You should make attempts to copy this behaviour as it brings the web inline with an established UX pattern in computing software.
Nothing a user enters should be lost if it can be helped.
PS - I would look into local storage instead of cookies, it's supported by 99% of clients and is much more flexible, there's a lot more space (more than 4k) and it's more persitent: