This might be an edge case but I think there will be more folks who notice that if they are using Lightning and have the Quote related list added to Opportunity they will not be able to create a new Quote in SF1 but will have this functionality in Lightning desktop. My team encountered this issue recently unfortunately after we had already gone live and promised the users this functionality on mobile. It turns out that SFDC R&D needed to remove the button from SF1 for undisclosed reasons but I was able to get that far with their tier 2 support team who were very helpful and did a bit of researching for us to discover the cause of the disappearing button. I am posting this as a Q&A with the hope that it proves useful to a fellow developer out there facing the same issue.
I was able to create a workaround using a Lightning Component Action and I have written about my solution and provided links to my repo with the example code here:
I hope this is useful for someone else who might get stuck with the same issue. We have a heavy mobile user base so this was very important functionality to deliver. Happy coding!