At my work we use SDE databases to store our geospatial data with geodatabases and feature classes within the SDE database.
Is there a way on a certain feature class in the SDE database to get a version of that feature class from a certain date, so we can look back at our data and compare certain times to see change of features?
Yes, it is possible if you have Archiving enabled on that feature class.
Take a look at these link and see if they answer your question:
Geodatabase archiving—ArcGIS Help | ArcGIS Desktop
Working with historical versions—ArcGIS Help | ArcGIS Desktop