Drop down text field fillable and searchable, is it possible?

You can achieve something similar to what you described using this (paid-for) script I've developed that allows you to use a text field to filter the items of a drop-down field. You can find it here:

http://try67.blogspot.com/2012/11/acrobat-create-live-filtered-list.html

You can also get it from my new web-site, where's there's currently a "soft launch" sale (The discount code is available on the front-page):

https://www.try67.com/tool/acrobat-create-live-filtered-list

Hey Tracey,

Thank you for reaching out.

As I understand, you wish to make the drop-down list searchable so that you can type in the first letter and it will search the matching word in the list. 

Currently, there is no such option to set up a searchable drop-down list by default in Acrobat. 

However, you may try to achieve this by using a script. 

Hope the information helps.

Thanks,

Meenakshi