Mozilla Future Releases has published the article Windows 10 and User Choice, which talks about some the changes that have occurred with Firefox as a result of Windows 10. Besides Windows 10 making Edge your default browser (unless you do a custom install), web searches using Cortana are done though Bing. The article goes on to explain how they have been able to workaround some these changes. But first, they talk about the UI change in regards to the search feature for the Windows 10 version of Firefox:
User choice is a core principle with which we design our products. In particular, we’ve found that the best way to design products is to craft experiences where our users understand the choices they are making and ensuring those choices are respected.
A recent example is how we evolved our strategy around search in favor of a more geographically targeted approach to search. First, when we changed the default search provider shipping with Firefox in a relevant geography, if a user had chosen a specific search provider as default before the switch, we respected that choice and made no change to that user’s default. Second, we redesigned the user interface to make it easier to both change the default search engine as well as choose different search engines on a per-search basis with a single click.
The irony here is Windows 10 users DON’T have a choice in getting the new search UI. From what I have read on the mozillaZine Firefox Builds forum, some folks don’t like this change and there seems to be no (easy) way to undo it.