Can I install insulation behind a shower stall that is already in place?
There are two issues: 1) yes, you should add insulation, and 2) no, it should not have a vapor barrier. 

1) Yes, insulation will help with the temperature comfort level you’re complaining about. It will help to maintain a constant temperature. 

It will be difficult to install because it’s not very accessible. 

2) A vapor barrier should not be installed. 

Most people don’t understand that “vapor” moves both ways through a wall. That is to say, vapor moves from the warm side to the cool side. As the seasons change, vapor will move through the wall reaching its Dew Point, and turning from a vapor to a solid (water). 

If this water is trapped in the wall, it could create dryrot or mold. With a vapor barrier, vapor will enter the wall but not be able to escape. In fact, poly sheeting can accelerate the problem and is no longer recommend, except in the coldest year-around climates. 

Here’s an article that explains it better:

https://www.energyvanguard.com/blog/75130/What-Happens-When-You-Put-a-Plastic-Vapor-Barrier-in-Your-Wall

It’s very important to understand this concept for bathrooms with excessive moisture. That moisture needs a way to escape from the wall. (Even the best installed poly sheeting will allow vapor into the wall around outlets, joints in sheeting, top and bottom plates, etc. )