In DOS and Windows System, an EXE File is an executable file with an .EXE extension. As far as I know you(almarwai) would be better to use not web hosting but file hosting. I'm not sure as for your request. Do search in Google for your requirements.
I would second the recommendation of VPS or a dedicated server like others as no shared hosting provider will allow you to host the exe files unless they are from a reputed vendor.
If you do not have any budget problem, windows dedicated servers are available with all possible configurations... but if you wish to get this started on testing purpose and have budget problems too, then I would suggest you to go for a good VPS company. You can find many of them recommended over there on WHT.
Also be sure to keep an eye on the vps offers displayed in the advt threads as many times a good deal strikes in those threads too