How to downgrade SQL Server 2012 Enterprise to 2012 Express?
The very first thing you would need to check on that instance would be for all the databases hosted, using any enterprise features from sys.dm_db_persisted_sku_features. In case the database is using any of such enterprise features, you will need to thoroughly verify , but not sure if express can get you there and most probably downgrade wont be that easy.

In addition its better to go through Supported Version and Edition Upgrades while you consider to change the edition and compare features.

There is no direct way to do the downgrade but you can follow the steps of copying the system databases of the enterprise edition instance to the instance of expressed one.Also making sure the new instance being the same with latest update to date with same patch details.

Please refer to below articles which will help you in analyzing how to analyse the downgrade process.

Downgrade enterprise SQL server to standard ( Steps can be somewhat same for express edition as well, just look for features that will support you're application in case you go with express)

Changing SQL Server Editions: Standard, Enterprise, Evaluation and More

Also, make note is good to test it out first for one of you're small servers on a test ENV with such downgrade activity.