Can I allow someone to download a file from my iCloud account with the URL address?

I am a teacher who teachess a computer lab of students (still running Windows XP) and I have been uploading pictures and files to my Comcast web storage, and then giving my students a TinyURL to download those files. Comcast has quit having that storage as of October 8. I didn't know about until I tried to upload some files last night (October 9).

I'm hoping my iCloud account can allow me to do the same thing. I am unfamiliar with iCloud otherwise. I still prefer to keep local control of most of my files, but I may be dragged, kicking and screaming, into the 21st century yet.

Thanks for any help you can provide.

Brian