Will an Ipad4 run a .exe file?

No. Exe files are Windows executables only. There are however methods to run them on Macs.

But iPads, or iPhones and iPods for that matter will not run them.

Any and all software that can be run on an iPad can only be obtained from the App Store. You can't download executable files from anywhere else and expect them to run let alone install.

No. The only way to install an application/program to an iPad is by downloading it from the App Store.

Welcome to the Apple Support Communities

EXE files only works in Windows, so they won't run on the iPad. The iPad uses iOS, and you can only install apps from the App Store

No.

You can run one on a Mac using emulation software or on a PC.

I just installed a file converter app from the market. Do you know what file types are listed for apps in the Apple Market?

Posting at the bottom of a thread that has been dead for 4 years certainly is not the best place to get it the notice it deserved.