When we start with SharePoint infrastructure lot of time SSL is not taken into consideration but at later point of time and surely in Production you should have SSL for encryption.
Since your users are used to HTTP URL you cannot ask every one of them to go to HTTPS from now on. The best is to redirect users automatically from HTTP to HTTPS. This article is not about how do this automatic redirection you can get to know the steps from here
We also did steps same as above but we faced some issues after which you might also get which depends on how your infrastructure has been set up
- Issues with OneNote : If your end users have stored OneNote in document library all of them will have HTTP URL as their source so after redirecting to HTTPS you cannot save it to HTTP anymore. If one of users save it with new URL then it will be saved as new OneNote file. This is a tricky situation as you cannot get the old file and all will have local copies. Best strategy is to have the latest OneNote saved before you do redirection and upload it as new one after redirection.
- Issues with embedded links in files : If you have embedded links of MS Office documents in other documents then you will still be able to open documents but all of them will open in read only mode but usually you will have option to edit directly from them. Solution to this to update the links after redirection, there is no alternative to this. Good part is still you can open the file.
- Search issues : If you have HTTP URL as default URL in AAM or have used HTTP URL in search configuration then your search might break, you will not see any results but no error as well. To fix this you just use HTTPS URL at all places.
So these are things you need to consider if you plan for HTTP to HTTPS redirection.
Some other reference