Is that your shower?

I get cold in any open showers very cold.

You were asked a question about YOUR shower. How big is it?? If it is even slightly smaller than the one photographed, the answer is NO. There will be water everywhere. If you don’t like cleaning the shower glass....you will be mopping up the bathroom floor.

Is this your shower? Pretty simple question to answer.If this is your shower IMO cleaning the grout will be a much bigger job than a glass door and how you have designed this will have water everywhere with that rain head where it is . Where was the designer when this was planned IMO the door needed to be an integral part of the whole plan. It takes a few seconds to squeegee a glass shower wall and you already have one if this is your shower

No, not my shower. Just found a picture Of something similar that I want.

Might be able to do something like this

Do you have hard water in your area? I was advised to dry my tile to reduce potential grout concerns. Many of us with glass shower doors apply multiple coats of Rain X, which markedly reduces time spent cleaning glass. If you opt for no glass, secure an outstanding contractor/tile installer who will install correct slope and drain.