How to dynamically add values to a dropdown through workflow

If the dropdown is based on a List Lookup, then your workflow can simply add items to that list.

it might be possible but just for a choice control not bound to a list field. you would need to supply possible dropdown options as a semicolon separated list of values

see an exampe - https://community.nintex.com/thread/15319-checklist-based-on-value#comment-59806