Thanks Jason,
There are solution in the publishing process for hosted services in ArcGIS Online and ArcGIS Enterprise to set the timezone. If you are using data collected in a local time zone with ArcGIS Server, I'd suggest creating a tool that converts local time to UTC prior to publishing if you have than two fields.
We are working on some projects for setting a specific timezone for some applications. That being said, time can be incredibly confusing when people from varying timezone and experiences may be viewing your data, especially with public maps. Currently, using UTC as a standard time and converting to local timezone is a consistent way to share date and time information with users without requiring the users to perform time conversions. I'd like to know more about you specific project to understand your needs further.
Is the map that you are creating only accessible to some users who are all in the same timezone or is it also accessible to the public? If someone in a different timezone was viewing your data, what would be the best way for them to understand the timezone of the original data vs. the timezone that they are reading in the map? Should this be defined by the map creator or the map reader?
Thanks for your feedback,
-Kelly