We don't have a shower door on our shower. The odd drop of water escapes, but not much. Depends on the design. Re: cold, no, it isn't cold. Our master bath is relatively small, so the room warms up quickly, like a shower stall would. If the bathroom is huge cold may be more of a concern.

I did a search for 'doorless showers' here on this forum and came up with 18 threads. This is a very popular topic. All your questions shall be answered.

-Babka

Here is a link that might be useful: Doorless Shower threads

I am definitely one of those who likes the shower to heat up. No door would not work for me because bathroom is too large. How big is your bathroom?

Would be too drafty for me. (And my DH wipes down the glass!)